metadata: authors: 0: author: Sinha Roy,Sutirtha
1: author: Van Der Weide,Roy
count: India
docna: 0: docna: Poverty in India Has Declined over the Last
            Decade But Not As Much As Previously Thought
docty: Policy Research Working Paper
abstracts: cdata!: The last expenditure survey released by
            India&#x2019;s National Sample Survey organization dates
            back to 2011, which is when India last released official
            estimates of poverty and inequality. This paper sheds light
            on how poverty and inequality have evolved since 2011 using
            a new household panel survey, the Consumer Pyramids
            Household Survey conducted by a private data company. The
            results show that: (1) extreme poverty is 12.3 percentage
            points lower in 2019 than in 2011, with greater poverty
            reductions in rural areas; (2) urban poverty rose by 2
            percentage points in 2016 (coinciding with the
            demonetization event) and rural poverty reduction stalled by
            2019 (coinciding with a slowdown in the economy); (3)
            poverty is estimated to be considerably higher than earlier
            projections based on consumption growth observed in national
            accounts; and (4) consumption inequality in India has
            moderated since 2011.
display_title: Poverty in India Has Declined over
            the Last Decade But Not As Much As Previously Thought
listing_relative_url: /research/2022/04/33779233/poverty-india-declined-over-last-decade-not-much-previously-thought
topicv3: Poverty m1326687 695,Inequality and Shared Prosperity m1327655 700
publishtoextweb_dt: 2022-04-05T00:00:00Z
dois: 10.1596/1813-9450-9994
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 133
author_keys: 0: author_key: 1312512
1: author_key: 677092
model_extractions: Policy Research Working Paper 9994 Poverty in India Has Declined over the Last Decade But Not As Much As Previously Thought _Sutirtha Sinha Roy Roy van der Weide_ Poverty and Equity Global Practice & Development Research Group April 2022
Policy Research Working Paper 9994

# **Abstract**

The last expenditure survey released by India’s National Sample Survey organization dates back to 2011, which is when India last released official estimates of poverty and inequality. This paper sheds light on how poverty and inequality have evolved since 2011 using a new household panel survey, the Consumer Pyramids Household Survey conducted by a private data company. The results show that: (1) extreme poverty is 12.3 percentage points lower in 2019 than in 2011, with greater poverty reductions in rural areas; (2) urban poverty rose by 2 percentage points in 2016 (coinciding with the demonetization event) and rural poverty reduction stalled by 2019 (coinciding with a slowdown in the economy); (3) poverty is estimated to be considerably higher than earlier projections based on consumption growth observed in national accounts; and (4) consumption inequality in India has moderated since 2011.

This paper is a product of the Poverty and Equity Global Practice and the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http:// www.worldbank.org/prwp. The authors may be contacted at ssinharoy@worldbank.org and rvanderweide@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Poverty in India Has Declined over the Last Decade But Not As Much As Previously Thought<sup>_∗_</sup> Sutirtha Sinha Roy and Roy van der Weide<sup>_†_</sup>

Originally published in the Policy Research Working Paper Series on _April 2022._ This version is updated on _May 2024._ To obtain the originally published version, please email prwp@worldbank.org.

**Keywords:** poverty, inequality, India **JEL Classification:** I32

> _∗_ The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. The authors gratefully acknowledge financial support from the UK Government through the Data and Evidence for Tackling Extreme Poverty (DEEP) Research Program. Excellent research support was provided by Ruchi Avtar, Khushboo Chaudhary and Serene Vaid. The authors are most grateful to Peter Lanjouw for organizing a seminar to solicit valuable feedback from Gaurav Datt, Chris Elbers, Maitreesh Ghatak, Himanshu, Abhiroop Mukhopadhyay, Rinku Murgai, and Martin Ravallion, which has greatly benefited the paper. The authors are equally grateful to our colleagues Junaid Kamal Ahmad, Zoubida Allaoua, Surjit Bhalla, Andrew Dabalen, Indermit Gill, Kristen Himelein, Johannes Hoogeveen, Dean Mitchell Jolliffe, Aart Kraay, Nandini Krishnan, Christoph Lakner, Ambar Narayan, Odyssia Sophie Si Jia Ng, Pedro Olinto, Berk Ozler, Carmen Reinhart, Bob Rijkers, Paul Andres Corral Rodas, Carolina Sanchez-Paramo, Nayantara Sarma, Hans Timmer, Tara Vishwanath, Nobuo Yoshida, and members of the World Banks Global Poverty Monitoring Group and Office of the Chief Economist for South Asia at the World Bank for their very helpful comments and suggestions.

> _†_ ssinharoy@worldbank.org; rvanderweide@worldbank.org
# **1 Introduction**

Household consumption expenditure surveys conducted by the National Sample Survey (NSS) organization are the main source of poverty and inequality statistics in India. These surveys support the development of major data-driven policies in India and are used as inputs in the estimation of GDP and India’s consumer price index (CPI).<sup>1</sup> The latest NSS expenditure survey that is publicly available for India is from 2011. As the Indian economy has undergone significant changes since then, the release of the 201718 round of the survey had been eagerly anticipated. Unfortunately, it was ultimately decided to withhold the unit level survey data and its main results.<sup>2</sup> Using leaked estimates of the empirical distribution function of household consumption, Subramanian (2019) shows that poverty increased in rural India between 2011 and 2017 and that consumption inequality moderated (both in rural and urban areas). The rise in rural poverty neither sits well with consumption trends reported in national accounts data nor with proxy indicators of household welfare derived from official and non-official sources (including labor force surveys, surveys on agricultural household incomes, national family and health surveys of DHS, nighttime lights, etc.).

In the absence of an official consumption survey, several studies have attempted to fill the gap in poverty and inequality data by exploiting alternative data sources. Newhouse and Vyas (2019) and Edochie et al. (2022) impute household consumption into different choices of non-expenditure surveys, namely the Survey of Expenditure on Services and Durables (conducted in 2014-15) and the Survey on Social Consumption on Health (conducted in 2017-18). Chen, et al. (2018) and Felman, et al. (2019) predict growth in mean household consumption based on national accounts data.<sup>3</sup> Bhalla, Bhasin and Virmani (2022) build predictions using night-time lights and changes in state gross domestic product data. Desai (2020) estimates poverty using consumption data obtained from a sub-round of the India Human Development Survey conducted in 2017<sup>4,5</sup> . All studies report a reduction in headcount poverty in India in the years

> 1Given that approximately 18 percent of the worlds population lives in India, its poverty and inequality numbers are also crucial for any efforts to track global poverty, see e.g. Chen and Ravallion (2010).

> 2The government raised concerns about the quality of the NSS-2017 household expenditure data according to the following press release: https://pib.gov.in/Pressreleaseshare.aspx?PRID=1591792.

> 3The relationship between poverty reduction and growth in India has been studied earlier in Datt and Ravallion (2011). See also the cross-country study by Ravallion (2012) on the intricate relationship between poverty and growth.

> 4Desai (2020) is limited to only three states in India, namely Uttarakhand, Bihar and Rajasthan.

> 5More recently, Gupta, Malani and Woda (2021b) use consumption data from the Consumer Pyramid Household Survey to directly estimate poverty for 2019. However, the paper makes no attempt to make newly obtained estimates of poverty comparable to estimates for 2011, preventing assessments of how poverty evolved after 2011

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following 2011 - contradicting the headline estimates of the leaked 2017 NSS survey. These apparently contradictory results, combined with restrictions on the release of the NSS-2017 consumption survey, has given rise to a new Great Indian Poverty Debate, a sequel to the debate from the 1990s (Deaton and Kozel, 2005; Kijima and Lanjouw, 2005).

The private sector has recently stepped in by fielding its own household consumption survey called the Consumer Pyramid Household Survey (CPHS). The CPHS may be preferred to alternative data sources used to date for several reasons (but remains second-best to the NSS household consumption expenditure survey for poverty measurement). First, it collects detailed expenditure information on about 115 items, offering household consumption data for the first time since the NSS-2011. Second, the CPHS contains a panel of approximately 174,000 households that covers 28 states representing over 95% of India’s population. Third, it is conducted continuously at four-month intervals since its launch in January 2014. This opens the possibility of tracking poverty and inequality at a frequency higher than what has been traditionally feasible based on NSO’s quinquennial consumption expenditure surveys. The CPHS is already being used in empirical research. Chanda and Cook (2020) and Chodorow-Reich et al. (2020) use it to estimate the impacts of the demonetization policy, Deshpande (2020) and Gupta et al. (2021a, 2021b) have used the survey to quantify the impact of Covid induced lockdowns on labor market indicators, and Ghatak et al. (2020) employ the CPHS to study rates of consumption and savings in low-income households in India.

Despite these advantages, the CPHS also has its limitations. The CPHS adopts a measure of consumption that is not readily comparable to that of the NSS, stemming from differences in survey instruments. Furthermore, scholars have questioned the representativeness of the survey compared to NSS surveys, due to differences in sample design and geographical coverage (for instance Somanchi and Dreze 2021 and Somanchi, 2021). Both of these differences will have important impacts on poverty estimates for India (e.g., Deaton, 2003).

The objective of this paper is two-fold. First, we conduct a comprehensive examination of potential biases in the CPHS survey and propose adjustments to the survey weights that transform the CPHS into a nationally representative dataset. The outcome of this work will hopefully serve as a public good for anyone looking to use the CPHS for their empirical research. Second, we use the reweighted CPHS to construct NSS-compatible measures of poverty and inequality for the years 2015 to 2019. The challenge in this second objective is similar to that of Tarozzi (2007) which seeks to establish comparability in welfare aggregates across rounds of NSS’ consumption ex3
penditure surveys that adopt different recall periods.<sup>6</sup> We consider two approaches to imputing NSS-compatible consumption into the CPHS. Our preferred approach identifies the relationship between CPHS- and NSSconsumption, and then use this relationship to convert observed CPHS consumption into NSS-type consumption (within the CPHS survey). As a robustness check, we also impute NSS-type consumption on the basis of non-expenditure predictors of consumption that are shared between the CPHS and NSS (i.e. demographics, education, employment, dwelling characteristics, and asset ownership). Both approaches yield qualitatively similar results. We validate our estimates of the levels and trends in poverty and inequality by means of an inclusive set of corroborative evidence that brings in every available source of official and non-official data that could help rationalize the trends in mean consumption, poverty and inequality in India over the last decade.

Our findings are as follows. First, the poverty headcount rate in India is estimated to have declined by 12.3 percentage points since 2011.<sup>7</sup> Our preferred estimates suggest that the poverty head-count rate is 10.2 percent in 2019, down from 22.5 percent in 2011. Second, reductions in rural areas are more pronounced than in urban areas. Rural and urban poverty dropped by 14.7 and 7.9 percentage points during 2011-2019. Third, urban poverty rose by 2 percentage point in 2016 (coinciding with the demonetization event) and rural poverty rose by 10 basis points in 2019 (coinciding with a slowdown in the economy). Fourth, we observe a slight moderation in consumption inequality since 2011, but by a margin smaller than what is reported in the unreleased NSS-2017 survey.<sup>8</sup> Finally, the extent of poverty reduction during 2015-2019 is estimated to be notably lower than earlier projections based on growth in private final consumption expenditure reported in national account statistics. Our analysis stops just before the 6Similar methods have been applied to estimate consistent poverty measures when recent household survey data is unavailable and older estimates are considered outdated (Douidich, et al., 2016); to report poverty rates at finer levels of spatial disaggregation (Elbers, et al., 2003); and, to validate official estimates of poverty when comparability of data across surveys is compromised due to changes in instruments (Tarozzi, 2007).

> 7This suggests an extension of the steady progress observed in India over the last two decades, see e.g. Gravel and Mukhopadhyay (2010). However, Dreze and Sen (2012) note that this progress does not extend to all indicators as growth in select nutrition and health indicators, for example, have been more muted. Similarly, Ravallion (2016) notes that despite high growth and a fall in headcount rates in developing countries, the minimum levels of living for the global poor has not moved by much over the past three decades. Castello-Climent and Mukhopadhyay (2013) and Castello-Climent et al. (2018) show that in growth in India is sensitive to changes in tertiary education levels -- suggesting that changes in higher levels of education can impact poverty through the growth channel.

> 8The observed reductions in inequality and poverty are accompanied by major expansion of social security programs in India (e.g. school meals, child care services, employment guarantee, food subsidies, and social security pensions) in the past (see e.g. Dreze and Khera (2017)); and, an expansion of household access to bank accounts, cooking gas, access to toilets, electricity, housing, etc in recent periods, see e.g. Subramanian and Felman (2022).

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lockdown measures were imposed due to Covid-19 and therefore cannot speak to changes in poverty headcounts in the aftermath of the pandemic.

The rest of the paper proceeds as follows. Section 2 provides a detailed overview of the known differences between the survey instrument and sample design of CPHS and NSS and sets up both datasets to achieve closest possible comparability based on this knowledge. Section 3 examines the results of the reweighting exercise while Section 4 introduces our two approaches to estimating NSS-consistent measures of consumption. Section 5 reports headline poverty and inequality estimates and reports the results from robustness checks. Section 6 corroborates our findings using a range of independent data sources. We conclude in Section 7.

# **2 Data**

## **2.1 Consumer Pyramid Household Survey (CPHS)**

The CPHS is a stratified multi-stage survey with towns and villages from the 2011 population census as its primary sampling units (PSU) and households as its ultimate sample unit (USU). CPHS’ first stage stratum is a spatial unit called Homogeneous Region (HR), which is a set of contiguous districts with similar agroclimatic conditions, urbanization levels, female literacy rates and number of households. The latest round of CPHS consists of 102 HRs spread over 28 states and 514 districts in India (out of total of 36 states and 718 districts in India), with each HR further divided into rural and urban sub-strata. The latest round of CPHS’ rural sample comprises 63,430 households selected randomly from 3,965 villages and 110,975 households from 7,920 urban census enumeration blocks (CEBs).

The CPHS’ consumption module contains monthly household expenses for about 115 unique items. A quarter of these relate to food, while others include expenditures on clothing, footwear, cosmetics, toiletries, appliances, restaurants, utilities, transport, communication, education, health, monthly loan repayments and other miscellaneous items. CPHS interviews households three-times a year, at four-month intervals referred to as waves. Households report item-wise consumption for each of these four months. Household interviews are scheduled such that survey estimates are nationally representative for each month of the CPHS wave. In addition to consumption expenditures, CPHS collects data on demographic information, incomes, employment status of members, asset ownership and consumer sentiments of the household. The CPHS does not conduct a listing exercise. Instead, it uses household and population growth projections from Registrar General and Census Commissioner of India to calculate household and 5
population level sampling weights.

The CPHS’ sample has evolved over time with household dropping out of the original panel and new replacement households being added. A notable number of households were deleted and added to the CPHS panel during the first five waves of data collection (Figure 1). For that reason, we begin our analysis of CPHS data from 2015-16.<sup>9</sup> There are large net additions to the rural panel during the third wave of 2017. The number of sampled districts increased from 422 to 503 between the second and the third wave of 2017. The newly added districts are concentrated in the comparatively poor and rural areas of the country (with a 2011 mean household consumption per capita that is 18 percent lower when compared to the districts that were already part of the sample).

Response rates in the CPHS vary between 80.6 and 87.6 percent over the 2014 to 2019 period. The highest non-response rates are observed during the pandemic-induced lockdown of 2020. The fraction of households from the first wave of 2014 that remained in the panel until December 2019 is 16.9 percent.<sup>10</sup> On average, the probability that a household will survive the panel is halved after about 7 waves of data collection. Further information on the sample is available on the CPHS’ official website.

# **2.2 NSS surveys and other data sources**

We use a range of secondary data sources to correct for biases in the CPHS and to validate our estimates of poverty and inequality for the 2015 to 2019 period.

_NSS consumption surveys_ : The 68<sup>th</sup> round of NSS conducted between July 2011 and June 2012, is the latest official source of consumption data publicly available for India. The survey reports consumption expenditure values with a 30-day recall period<sup>11</sup> and consists of a sample of over 100,000 households spread across all Indian states. Survey estimates are representative at the district level. The poverty headcount rate at the $1.90 poverty line is 22.49 percent and the Gini coefficient is 35.71 using consumption per capita based on uniform recall period. We also use select moments derived from the leaked cumulative distribution function that is estimated from the 2017 NSS consumption expenditure survey round for robustness checks.

_Other official surveys_ : Despite there being no contemporaneous NSS and CPHS expenditure surveys, there are three official non-expenditure surveys that allow us to 9Vyas (2020) offers a detailed account of the execution challenges by the survey team until the first wave of 2015, especially related to inclusion of excess CEBs in the urban sample.

> 10CMIE makes an attempt to revisit households that are locked on the same day or sometimes the next day in villages. In urban areas, repeated re-visits are conducted spread over several days. If households are consistently locked or unoccupied over three waves, they are dropped from the panel.

> 11We continue the existing practice of measuring poverty and inequality from older NSS rounds based on the uniform recall period (URP)

6
<!-- Start of picture text --> 15.0% Changes in sample composition based on<br>release of new census data and field level<br>challenges<br>Expansion of the rural<br>10.0% sample<br>5.0%<br>0.0%<br>-5.0%<br>-10.0%<br>% addition % deletion<br>-15.0%<br>Percentage of samples added or deleted<br><!-- End of picture text --> Figure 1: Percentage of samples added and deleted over survey waves. Notes: Based on Vyas (2020).

observe changes in socioeconomic variables since 2011. These are: (i) periodic labor force surveys (PLFS) of 2017-18, 2018-19 and 2019-20; (ii) the situation assessment of agricultural households (SAAH) of 2013 and 2019; and, (iii) the all-India Debt and Investment Surveys (AIDIS) of 2013 and 2019. The PLFS provides estimates of wage growth for casual and salaried wage workers, while AIDIS surveys track the evolution of physical and financial assets ownership overtime. The SAAH surveys allow us to study income inequality across agricultural (and predominantly rural) households. Following Himanshu (2019), we use these surveys to construct updated estimates of consumption, earnings, income and asset inequality.

The PLFS furthermore contains a single self-reported expenditure variable referred to as “usual household consumption expenditure”, which may serve as a proxy for the respondent’s monthly consumption. Mehrotra and Parida (2021) have used this “usual consumption expenditure” variable to document a large increase in headcount poverty in 2019-20. In Appendix 5, we examine this welfare aggregate and detect the presence of significant bunching of consumption around multiples of Rs. 1000 - consistent with theory of satisficing documented in Krosnick (2018). Our simulations suggest that these rounding off errors can have a considerable impact on estimates of poverty and 7
inequality.

We also use the National Health and Family Surveys (NFHS) to obtain estimates of changes in consumer durable assets and access to public services, such as electricity, water and toilet on household premises. We follow Somanchi (2021) and use the publicly released state-level aggregates of 14 states from the NFHS’ 2019 round to validate our reweighting strategy (see section 3).

Finally, we use changes in real rural wages reported in Kundu (2019) to validate estimated changes in the consumption distribution for rural India observed after 2011.

_Non-official surveys_ : We rely on two private survey data sources to further our understanding of household consumption since 2014. The first is the India Human Development Survey (IHDS) subsample round, comprising of a sample of 4,828 households from three states of Rajasthan, Bihar, Uttarakhand and fielded during February to July 2017. The first two rounds of IHDS are nationally representative household panels with waves conducted in 2004 and 2011. Households interviewed in the third subsample round of 2017 are part of IHDS’ original panel (Desai, 2020). Consumption aggregates from IHDS are based on a basket of 52 items. Average national consumption growth between 2004 and 2011 based on IHDS is 3.8 percent compared to compared to 3.5 percent growth reported in NSS. Historically, the mean consumption growth from the two surveys have closely tracked each other.

We also use publicly reported quarterly growth estimates of fast-moving consumer goods (FMCG) from Nielsen to track consumption trends. These estimates are based on Nielsen’s extensive network tracking sales, stock and prices of FMCG goods across brick-and-mortar shops and online channels in rural as well as urban centers.

_National accounts and remote sensing data._ We use growth in private final consumption expenditure (PFCE) per capita based on national accounts and night-time lights data from 2014 to 2020 from Beyer, et al. (2021) to validate our main results. Nighttime light data are aggregated to the district level and measured in Nanowatts/cm2/steradian.

# **2.3 Differences between CPHS and NSS consumption surveys**

In this section, we systematically document differences between CPHS and NSS consumption surveys that hamper direct comparisons of consumption levels between the two surveys.

_Sampling differences._ First, the rural and urban substrata in the two surveys constitute different geographical units. The rural FSUs in the NSS’ 2011-12 survey were drawn based on 2001 population census village boundaries, whereas the rural FSUs in the CPHS are based on the 2011 round of the census. The number of statutory towns 8
in India has grown by 6 percent between 2001 and 2011 census rounds (ORGI, 2011) as villages evolved into towns, resulting in a divergence in the urban-rural classification between the two surveys. From a poverty measurement perspective this could matter because growth of smaller towns has an impact on rural poverty (Gibson et al., 2017). Second, larger villages and towns are more likely to be selected in the NSS, whereas differently sized villages have an equal probability of being sampled into the CPHS. More specifically, the NSS draws FSU locations based on population size. In comparison, the CPHS selects rural villages from the rural strata using simple random sampling; for urban areas, CPHS stratifies cities into four groups based on their population and then draws urban FSUs using simple random sampling. Within the FSUs from the CPHS, households have unequal sampling probabilities as households on the main street may have a higher likelihood of selection into the sample relative to other households (see Pais and Rawal, 2021; Dreze and Somanchi, 2021 for details).

Third, the NSS-2011 survey implemented a second stage stratification process, selecting a greater fraction of households in state-regions that had a higher proportion of non-agricultural occupations in rural areas and urban households with mean per capita consumption expenditure between the 1<sup>st</sup> and 6<sup>th</sup> decile based on the NSS’ 2009-10 expenditure survey. The CPHS in contrast, randomly selects households in rural and urban areas without second-stage stratification, with higher urban draws compared to rural. Despite comparatively larger urban samples, the absence of a second stage stratification in the CPHS means that representation of households from both ends of the income distribution is left to chance. In the NSS, representation of urban households from the 1<sup>st</sup> to 6<sup>th</sup> deciles of the distribution is embedded into the sampling design.

Fourth, the CPHS defines households as the physical unit where a group of individual members reside; whereas the NSS defines household as a group of individuals who normally live together and share a common kitchen. The CPHS’ definition implies homeless people or families living in construction sites are excluded in the survey. This choice could potentially further contribute to under-coverage of the poorest households in the CPHS.

Fifth, unlike the NSS, the CPHS does not conduct a listing exercise. Instead, it uses projections of household and population growth from India’s census organization to construct sampling weights. The NSS does conduct a listing exercise at the start of every round and uses this frame to estimate household level weights. Population weights in the NSS are calculated as the product of the household’s sampling weight and its household size; in CPHS population weights are based on the population projections and not the number of household members observed in the survey.

_Differences in instruments._ Sixth, the NSO uses a more detailed consumption mod9
ule comprising of over 345 items, compared to 114 unique items captured in the CPHS. Expenditures on household appliances, personal transport equipment, other durables are notably not covered in the CPHS consumption survey. Both surveys contain information on household asset ownership. Additionally, the NSS’ expenditure based on uniform recall period captures household consumption over the past thirty days, whereas the CPHS collects consumption based on the past four calendar months. Differences in recall periods across surveys can have large impacts on estimates of poverty (Deaton, 2003; Deaton and Dreze, 2002; Tarozzi, 2007).

Seventh, the CPHS household consumption aggregate includes expenditures on insurance premiums and loan repayments, which are excluded in NSS’ consumption expenditure aggregate.

# **2.4 Addressing differences in instrument design**

In this section we document the necessary adjustments we applied to the CPHS datasets in order to address the differences in instrument design between the two surveys. First, we pool the CPHS interviews conducted during the second and third wave of a calendar year and the first wave of the following year to match (as closely as we can) the NSS-2011 reference period of July 2011 to June 2012. The second wave of CPHS starts in May and the first wave ends in April, with households reporting consumption for the past calendar month. Accordingly, CPHS consumption reference period will correspond to April (the month prior to May, when interviews begin) through March of the following year(the month prior to April, the last month of interview). The 2019-20 round of the CPHS consumption overlaps with the first week of the covid induced lockdowns (as the lockdowns in India were imposed on March 24<sup>th</sup> , 2020), and as such may provide limited evidence on how household consumption, poverty and inequality were impacted at the start of the lockdowns<sup>12</sup> Second, we exclude districts that are covered by the NSS consumption survey but not by the CPHS to obtain geographical consistency in our analysis. The excluded non-overlapping districts represent about 4.8 percent of the country’s population in 2011. Third, in an effort to approximate the NSS’ 30-day uniform recall period, we retain item-wise household expenditures for the month preceding the CPHS survey and ignore values that are reported with a lag of two to four months. Fourth, we construct a harmonized basket of items across the two surveys. Expenditures on loan repayments, insurance premiums and household’s private transfers to emigrated members are discarded from the CPHS -- while expenditures on durables, household appliances, etc.

> 12All references CPHS consumption years in this paper refer to the financial year starting April to March. That is, CPHS 2015 refers to the corresponding months in 2015-16.

10
are discarded from the NSS consumption survey. On average, the harmonized basket of goods accounts for about 96 percent of per capita consumption expenditure in the NSS-2011. Fifth, we standardize CPHS’ custom industry codes by constructing a concordance with the national industrial classification (NIC, 2008). Sixth, we discard the longitudinal properties of the CPHS by randomly selecting one wave out of a possible three waves in a year.<sup>13</sup> We adjust individual level sampling weights for non-response using an adjustment factor provided in the CPHS. This non-response adjusted weight, by design, addsup to the Census’ population projections for a given year. We choose not to rely on these individual weights as due to the passage of time -- the last available census is now a decade old -- population projections are likely to become imperfect. One of these imperfections stems from faster than expected fall in fertility rates in 2019 reported in the recent National Family and Health Survey round of 2019-21<sup>14</sup> . Instead, we reconstruct individual level survey weights by multiplying household level weights (provided in the CPHS survey) and the household size (observed in the household roster) for each round.<sup>15</sup> This approach allocates the same sampling weight to each household member and relies on the population distribution observed in the survey rather than the Census’ estimated population distribution.<sup>16</sup> Henceforward, we refer to these reconstructed weights as reported CPHS weights and implement a reweighting procedure (that produced adjusted weights) to achieve national representativeness.

# **2.5 Addressing differences in sampling design**

Comparisons of selected statistics obtained with the CPHS with those obtained with several nationally representative surveys identify key biases that raises concern about measurement of poverty and inequality using CPHS data with reported weights. For this reason, we undertake a systematic reweighting exercise with the objective to transform the CPHS into a nationally representative survey (and thereby correct for these biases). Following recent literature (Wittenberg, 2009; Tack and Ubilava, 2013), we adopt the 13Not all households are interviewed in all three waves in a year, due to households being unavailable, locked at the time of survey or other reasons. For households that are visited more than once a year, we choose one visit at random.

> 14If the fertility rate falls to below replacement level, it signals that the population is stabilizing.https://indianexpress.com/article/india/fertility-rate-falls-to-below-replacementlevel-signals-population-is-stabilising-7639986/

> 15The individual level weights that are bundled in CPHS survey dataset are based on population projections from the Census. As these projections can become dated overtime, we observe the household size captured in CPHS’ survey roster and calculate individual weights as the product of CPHS’ reported household weight and its size.

> 16Note that the non-response adjusted household weights are still based on census’ household level projections.

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max-entropy approach advocated by Jaynes (1957).

The reweighting procedure consists of two steps. First, we use assets, demographic and education variables observed in the NFHS-2015 (as well as the CPHS) to reweigh all CPHS rounds from 2015 to 2019<sup>17</sup> . Second, we use demographic, education and labor market indicators observed in the PLFS rounds of 2017, 2018 and 2019 to further adjust the sampling weights in each round of the CPHS<sup>18</sup> . The second reweighting step allows us to account for changes in socio-economic indicators over time.

For the selection of target variables (on which to reweigh), we prioritize non-expenditure indicators that exhibit comparatively large biases in the CPHS relative to the benchmark surveys that are assumed to be nationally representative. An example of such a target variable is the share of undereducated adults (comprising of illiterate and below primary levels of education). We deliberately do not include all indicators that are shared between the CPHS, PLFS and NFHS in the set of target variables. This facilitates convergence of the max-entropy procedure (Zhang and Yoshida, 2022), and more importantly, sets aside a set of indicators that can be used to validate the reweighting exercise.

The adjusted sampling weights are obtained by matching the weighted means of the target variables between the CPHS and the benchmark representative surveys at the state-rural or urban levels (max-entropy minimizes distances between the weighted means obtained in the CPHS and the benchmark surveys). Following existing practices (e.g. Chen et al., 2018; Haziza and Beaumont, 2017; Kolenikov, 2014), the adjusted individual level weights obtained are winsorized at the 0.25<sup>th</sup> and 99.75<sup>th</sup> percentile level. We achieve national level representation by multiplying the resulting normalized weights with the rural and urban population populations of each state. The population estimates are obtained from the NFHS-2015 for 2015 and 2016 rounds; and from the PLFS 2017 to 2019 for the remaining periods. Finally, the household level weights are reconstructed by dividing the adjusted individual level weights by the household size observed in the survey.

17 We use the following set of target indicators for reweighting at the first step: dummy variables for ownership of air conditioners, cars, computers, refrigerators, television sets, two-wheelers, washing machine; dummies for household sizes 1 and 2, sizes 3 and 5; dummy variables for hindu, muslim, scheduled caste, schedule tribe, other backward classes households; total number of members less than 10 years old, over 60 years old; and, total members with below primary level of education, primary level and secondary level of education.

18 We use the following set of target indicators for reweighting at the second step: dummy variables for female headed household; scheduled caste, scheduled tribe and other backward classes households; dummy variables for household sizes 1 to 5; total members working in casual, salaried and self-employed jobs; total number of members less than 10 years old, over 60 years old; and, total members with below primary level of education, primary level of education and secondary level of education.

12
# **3 CPHS to benchmark Comparing surveys**

Our starting point is a CPHS dataset containing one observation per household per year, where consumption is reported with a one-month recall and individual level sampling weights reflect the observed population distribution. Nominal consumption expenditures in both the CPHS and NSS surveys are deflated to 2011-12-rupee prices using monthly CPI-IW and CPI-AL price indices for urban and rural observations, respectively. We also adjust for spatial price differences using 2011 PPP exchange rates from the International Comparison Program following Atamanov, et al. (2020).

## **3.1 Non-expenditure variables**

_Demographic characteristics:_ According to Somanchi (2021), the share of children under the age of 10 in CPHS-2019 is 8.9 percentage points lower than the official sample registration survey (SRS) of 2018. This under-coverage is balanced by shares of people aged 40 to 65 years being 11.9 percentage points higher in CPHS-2019 than SRS 2018. CPHS also reports a higher share of households with 2 to 5 members but undercounts households with either a single member or those with more than 6 members. Finally, the CPHS is seen to over-represent Hindu households compared to the benchmark surveys such as NFHS-4.

Figure 2 compares trends in key demographic indicators using the NSS-2011 consumption expenditure survey, the NSS-2014 survey on services and durable goods consumption and the PLFS surveys of 2017 through 2019 as the nationally representative benchmark surveys. The figure shows both the magnitude of the biases observed in the CPHS and the extent to which these biases are corrected by means of reweighting the CPHS. The distribution of household size and its trend estimated using the CPHS now closely match the estimates observed in the nationally representative NSS-surveys. The over-representation of Hindu households is also accounted for. The population shares for other religions similarly match with those observed in the NSS surveys. Biases observed in the composition of scheduled caste, scheduled tribes (and other classes), share of female headed units and households with extended family members living in the same house are also largely resolved through reweighting.

The one demographic variable for which a bias persists is the share of members aged between 0 and 18 years for which a gap of up to 5 percentage points between the CPHS and the NSS-surveys is observed.

_Asset ownership and access to services:_ Somanchi (2021) also documents that the shares of households with access to electricity, water, toilet and ownership of a television and refrigerator are notably higher in the CPHS -- 2015 and 2019 compared to the 13
<!-- Start of picture text --> 3Household size= 1 2.Household size=2] , 22Household size=3/ ”Household size=4/ aaHousehold\\* size=5 Household size= 6 ® Hindu~\.<br>4 : / \7 .<br>8 / _/ 8 q Py<br>is]<br>-~~S “ \ 8<br>° 3S = oy N<br>egigeesSeeeasRRRRARA egigeesSseeasRRRRRA egzeesSeseeasRRRRARA SseeeasRRRRARegezge8 esfeeqeeseeasRARRRRA ef22eR8SeseeasRRRRARA efreeRSeseeesRARRRARK<br>year year year year year year year<br>== Muslim aco Christian Soa Sikh Ss3 Jain 2Ss3Buddhist 5e Other religions 2sSch. Tribe<br>xs Wy g /¥ 3 8 Seg >, oss 2 at<br>22 2 g 3 © y;<br>= ays - “v4 x 2- 2= oe Sa _ an LY~ 5 \\<br>co o $s s o o .<br>eateas SAareas eateas sateas Sateasg sateen esateas<br>eseseegRRRRRA SeseeaagRRRRRA seesegRRRRRR SeseegRRRRARA eessegRRRRRA eeseegRRRRARA eseseegRRRRRR<br>year year year year year year year<br>a Sch. Caste z Oth Back Class S Other \caste Extended HH Share of 0-18 age —Ey Share of 61+ age 2 Female HoH<br>q XN \ ©” Pe*<br>“ 7 g< / ”8 \ ”. _ o ~ 25 \ = / /<br>/ \ /<br>2 2 = o wo wo o o<br>7 ea reas a ea teas N ea teas NX en teas N eateas ad eanteoane Se ean reas<br>SsesssasRRRRARA SssssaesRRRRARA SsessesgaesRRRRARA SsesssqsRRRARARAR SsssesesRRRRRA SsssegsRARRRA SsessseesRRRRRR<br>year year year year year year year<br>——®——._ Benchmark NSS ——®——_ Reweighted CPHS —-—-—-—- Reported CPHS<br><!-- End of picture text -->
with NFHS as benchmark. A candidate reason for this discrepancy is the difference in instrument design (these indicators are not in the set of targeting variables). In the NFHS, access to water and toilet within the household premises are collected through a detailed list of options, eliciting specific types of water sources and toilet waste disposal technologies available to the household. The CPHS in contrast, collects this information through binary yes or no questions without distinguishing between sources or disposal methods.

Comparison of CPHS and NFHS in 2019 (restricted to 14 states where asset ownership and public service access data is presently available) serves as a validation, as the reweighting for this year does not include asset ownership or access to services as target variables (these indicators are not available in the PLFS-2019). The results in Panel (b) of Figure 3 confirms the bias correction that is achieved for these non-target variables.

The largest gap in asset ownership between the CPHS and NFHS 2019 is for households owning television sets (10 percentage point) and air conditioning units (6 percentage points). The reweighting procedure does however reduce the bias by a significant margin: without reweighting, households owning TV sets would be 24 percentage points higher in the CPHS.

_Education levels:_ Undereducated people are severely under-represented in the CPHS with only 2 percent of the 2018 adult population (ages 15 to 49 years) having not received a formal education. By comparison, the periodic labor force survey (PLFS) from the same year estimates that the share of adults without formal education is 17 percent. By 2019, adults without formal education are virtually eliminated from the CPHS sample, while the PLFS-2019 continues to estimate this share of the population at approximately 17 percent. Somanchi (2021) similarly observes that female illiteracy is estimated with a significant bias in the CPHS (in selected states the mean values from the CPHS-2019 are as much as 45 percentage points lower than what is observed in the NFHS-5).

Figure 4 compares adult education levels (ages 15 to 49) in CPHS and PLFS for 2017 to 2019. The share of adult education attainment at the state level observed in the CPHS is plotted against the shares observed in the benchmark PLFS survey. Estimates above (below) the diagonal indicate states where education shares are estimated to be higher (lower) in the CPHS relative to the PLFS. Panel (a) of Figure 4 shows population shares of adults with below primary level education (which includes those with nonformal education as well non-literates). Panels (b) to (d) compare state level shares of primary, secondary and higher educated adults, while panel (e) plots the share of adults with graduate, certificate or post-graduate levels of education.

15
<!-- Start of picture text --> 100%<br>80%<br>60%<br>40%<br>20%<br>0%<br>Electrified PremisesToilet AccessWater Television Refrigerator ConditioningAir WheelerTwo Car Computer WashingMachine Pucca Wall Pucca Roof<br>Reweighted CPHS 2015 NFHS, 2015 Reported CPHS 2015<br><!-- End of picture text --> <!-- Start of picture text --> 100%<br>80%<br>60%<br>40%<br>20%<br>0%<br>Electrified PremisesToilet Water Access Television Refrigerator ConditioningAir Two Wheeler Car Computer WashingMachine Pucca house<br>Reweighted CPHS 2019 NFHS, 2019 Reported CPHS 2019<br><!-- End of picture text --> Figure 3: Access to services and asset ownership: NFHS and CPHS 2015 (panel (a); top), NFHS and CPHS 2019 (panel (b); bottom) Notes: Figure shows asset ownership shares and access to public services. Electrified households in CPHS are defined as those that pay non-zero amounts towards electricity; in NFHS these include households possessing an electrical connection. Toilet in premises in NFHS includes all households that do not have a toilet facility or conduct open defecation. Water in premises in NFHS includes those that have piped water in dwelling unit or use improved water sources. Pucca houses are those that have both pucca walls and pucca roofs. NFHS 2019 all-India estimates are produced by multiplying state-level ownership shares with estimated number of households reported in state-level fact sheets by DHS. Graphs highlighted with a red box denote indicators that were not included in the set of target variables for reweighting. All indicators in 2019 belong to this group.

Overall, reweighting has helped close the biases for these education variables that are observed in the CPHS when using the reported weights. Discrepancies in education 16
levels are most notable in states where illiteracy (or below primary level education) among adults is high. Reweighting is seen to be more successful in correcting biases in 2017 and 2018 than in 2019. But even in 2019, reweighting comes a long way in reducing the bias in states with high shares of illiterate or non-formal education. The estimates for higher education levels are largely scattered along the diagonal, confirming the successful bias correction. Figure 1 in Appendix 1.1 shows that the large bias in female illiteracy using reported CPHS data as documented in Somanchi (2021) is largely resolved after reweighting.

The NSS survey on education consumption conducted in 2017-18 provides another opportunity to compare education statistics derived from the (reweighted) CPHS against. As this survey is not used in the reweighting procedure, this comparison helps provide external validity of the adjustments made to the sampling weights. Panels (a), (b) and (c) from Figure 5 show the results for all adults, males and females above the age of 15, respectively. Reassuringly, all education level shares obtained using the adjusted CPHS sampling weights are within 1 percentage points from the benchmark survey. This denotes a notable improvement compared to the estimated obtained using the reported CPHS weights.

_Labor force indicators:_ Abraham and Srivastava (2019) observe a 3.2 percentage point gap in labor force participation rates among males between the CPHS-2017 and the PLFS from the same year. Labor force participation rate for females in the CPHS are about half that of what is estimated by the PLFS. Basole, et al.(2021) finds that the average real incomes in the CPHS of 2018 are about 30 percent higher when compared to the PLFS from the same year<sup>19</sup> . Despite the higher average incomes, wage inequality is lower in the CPHS relative to the PLFS: estimates of the Gini coefficient of income inequality for the two surveys are 0.42 and 0.44, respectively (excluding zero wage earners). Our analysis furthermore finds that the share of casual wages workers is higher in the CPHS than in the PLFS.

Figure 6 shows log monthly salaries and log daily wages for both the CPHS and benchmark surveys (these indicators are not included in the set of target variables used in reweighting). Reweighting closes the gap in monthly salaries and daily wages that is observed when using reported CPHS weights. The bias correction is larger for rural than for urban wage incomes. Unlike Basole, et al.(2021), we exclude income from self-employment in our analysis as determining profits from work requires detailed enumeration of cost and revenue parameters of an enterprise -- which are not recorded in either survey.

Reweighting is also seen to account for the gap in wage inequality between the CPHS 19Basole, et al. (2021) include earnings from self-employed work in their analysis.

17
<!-- Start of picture text --> below primary education shares<br>2017 2018<br>~” °. © ;<br>N e e<br>Q ° Pew «“*** al « o% « oh. x x x<br>x a<br>oO 0 A 2 3<br>2ow 2019<br>x= .<br>Ds<br>” A ee<br>° © wo eo ex KK OX x<br>0 A 2 3<br>share in PLFS<br>@ Reweighted CPHS x Reported CPHS ——— 45-deg line<br><!-- End of picture text --> <!-- Start of picture text --> secondary education shares<br>2017 2018<br>x @<br>©.<br>”Ed<br>.<br>no” °<br>rea a a oe<br>[S} 3 4 5 6<br>Ss@oo 2019e @<br>;<br>*: e «?, e<br>°<br>34 5 6<br>share in PLFS<br>@ Reweighted CPHS x Reported CPHS ——— 45-deg line<br><!-- End of picture text --> <!-- Start of picture text --> primary education shares<br>2017 2018<br>~”, e* ony<br>N we” - O xxx xe xno =<br>Q o e<br>x op<br>oO .05 A 15 2<br>ge 2019<br>x=ow.<br>Oe<br>~ e* 3x" x a x x<br>°<br>05 A 15 2<br>share in PLFS<br>@ Reweighted CPHS x Reported CPHS ——— 45-deg line<br><!-- End of picture text --> <!-- Start of picture text --> higher secondary education shares<br>2017 2018<br>Q<br>a”“. sennax ta — were@ eh<br>rea a<br>[S} 05 1 15 2 25<br>So@ 2019<br>Go” . oteo .<br>°<br>05 1 15 2 .25<br>share in PLFS<br>@ Reweighted CPHS x Reported CPHS ——— 45-deg line<br><!-- End of picture text --> <!-- Start of picture text --> graduate and above education shares<br>2017 2018<br>Q<br>+<br>”“-. * ee e xxe*6 °e<br>n * *<br>zxQo rr<br>[S} A 2 3 4<br>£<br>@Bo 2019<br>Be<br>~ e<br>ac}<br><:.eRe x x<br>°<br>A2 3 4<br>share in PLFS<br>@ Reweighted CPHS x Reported CPHS ——— 45-deg line<br><!-- End of picture text -->
<!-- Start of picture text --> 46% 450,<br>38% 37%<br>32% 32%<br>14%<br>72% 11% 11% 11%<br>Not literate+primary middle + secondary higher secondary graduate +<br>mReweightedCPHS NSS 2017-18 Reported CPHS<br><!-- End of picture text --> <!-- Start of picture text --> 40%<br>38% 37% 36% 36%<br>30%<br>17%<br>13% 14% 13%a0 13% 14 0%<br>Not literate-+primary middle + secondary higher secondary graduate +<br>mReweightedCPHS Mm NSS 2017-18 Reported CPHS<br><!-- End of picture text --> <!-- Start of picture text --> 54% 530%<br>47%<br>34%<br>29% 28%<br>12%<br>Not literate-+primary middle + secondary 9%highero, lI10%secondary 8%graduate8% +g%<br>mReweightedCPHS Mm NSS 2017-18 Reported CPHS<br><!-- End of picture text -->
<!-- Start of picture text --> 10.2<br>10<br>ya<br>ia 98 _<br>4sH - --""7<br>& oe<br>2 96 5<br>4aanto} —_—_i<br>94<br>9.2<br>9<br>2017,Rural 2018, Rural ~—-2019,Rural 2017,Urban 2018, Urban 2019,Urban<br>— Reweighted CPHS ——PLFS --- Reported CPHS<br><!-- End of picture text --> <!-- Start of picture text --> 6<br>weer<br>i<br>58 a<br>»ap=a 56 < =<br>c o<br>54ey a“<br>5.2<br>5<br>2017,Rural 2018, Rural ~—«-2019,Rural 2017,Urban 2018, Urban -2019,Urban<br>—Reweighted CPHS ——PLFS --- Reported CPHS<br><!-- End of picture text -->
<!-- Start of picture text --> 0.46<br>0.4 ———— ae<br>aS.gg8ga oomomen eens eee mee<br>© o4 Tse<br>0.38<br>0.36<br>2017 2018 2019<br>—Reweighted CPHS ——PLFS --- Reported CPHS<br><!-- End of picture text --> <!-- Start of picture text --> 0.29<br>0.28<br>0.27<br>FIg g 8 0.26 w AP ten aon ‘Ss.S<br>[S} 0.25 SS<br>a SS<br>6 s<br>0.24 SN<br>.<br>0.230.22 OO<br>0.21<br>2017 2018 2019<br>—Reweighted CPHS ——PLFS --~ Reported CPHS<br><!-- End of picture text -->
(Table 1). The reverse is observed in 2016-17. The absence of a clear pattern could partly stem from the fact that data from national accounts are themselves a source of contention (see e.g. Subramanian, 2019 and Goyal and Kumar, 2020 for details).

In Figure 8, the variance of log consumption per capita in the CPHS is lower than the variance observed in the NSS-2011 (on average 0.267 in the CPHS compared to 0.368 in the NSS-2011). The gap in consumption inequality is larger in urban areas. The Gini coefficient of inequality obtained using reported CPHS weights would rank urban India at par with Sweden, the 25<sup>th</sup> most equitable country in the world. By comparison, the NSS-2011 would rank urban India around the 60th most unequal country in the world.

The third moment of the log consumption per capita distribution is also markedly lower in the CPHS when compared to the NSS-2011. Figure 9 compares the third moment between the two surveys for urban and rural separately<sup>21</sup> . The gap in the third moment is larger in urban India, and larger than the gaps observed for the second moment (Figure 8). The second and third moment of log per capita consumption in CPHS are on average about 27 and 70 percent lower than the respective moments from the NSS-2011.

||Mean per|Private fnal|||
|---|---|---|---|---|
||capita|consumption|||
||consumption|expenditure|Growth in|Growth in|
||expenditure|per capita|survey|nominal|
||(MPCE,|(PFCE,|nominal|PFCE per|
|Year|nominal)|nominal)|MPCE|capita|
|2015-16|2193|6334|||
|2016-17|2315|7026|5.6%|10.9%|
|2017-18|2558|7638|10.5%|8.7%|
|2018-19|2846|8457|11.3%|10.7%|
|2019-20|3143|9179|10.4%|8.5%|

Table 1: Comparison of levels and trends in nominal consumption per capita in CPHS and National Account Statistics (NAS). Notes: Per capita consumption estimates are in nominal terms. Private final consumption expenditure is based on Statement 1.12 of national accounts statistics (NAS). The population estimates are also from NAS. Consumption per capita in CPHS is approximately 32 to 34 percent of PFCE per capita from NAS across years.

Comparing expenditure and non-expenditure statistics derived from the CPHS to

> 21Defined as _E_ [( _x − E_ ( _x_ ))<sup>3</sup> ] where _x_ is the log consumption per capita

22
<!-- Start of picture text --> 04<br>0.35<br>0.25 ae<br>0.2<br>2015 2016 2017 2018 2019<br>—Reweighted CPHS --- Reported CPHS ——NSS-2011<br><!-- End of picture text -->
<!-- Start of picture text --> 0.14<br>0.12<br>ees<br>g<br>a¢53S o1<br>8<br>§ 0.08<br>88<br>On<br>Re)<br>% 0.06<br>g<br>8<br>5 0.04<br>B<br>0.02<br>)<br>2015-16 2016-17 2017-18 2018-19 2019-20<br>—NSS-2011 —=CPHS<br><!-- End of picture text --> <!-- Start of picture text --> 02<br>eee<br>0.18<br>= 016<br>&§<br>3 0.14<br>o<br>8<br>012<br>8 o1<br>on<br>Re}<br>a2 0.08<br>g<br>8<br>not& EI 0.06 a<br>© 0.04<br>0.02<br>0<br>2015-16 2016-17 2017-18 2018-19 2019-20<br>—NSS-2011 —=CPHS<br><!-- End of picture text -->
<!-- Start of picture text --> 0.25<br>02 TT SS<br>0.15<br>04<br>0.05 a<br>0<br>2015 2016 2017 2018 2019<br>—Reweighted CPHS --- Reported CPHS +=——NSS-2011<br><!-- End of picture text -->
<!-- Start of picture text --> 0.2<br>0.15<br>01<br>0.05 ---------------->> es<br>0<br>1987 1993 1999 2004 2009 2011 2017<br>—NSS Rural ——NSS Urban --- Rural Reweighted CPHS = --=- Urban Reweighted CPHS<br><!-- End of picture text -->
<!-- Start of picture text --> 15% 0.6<br>0.583<br>0.567 0.58<br>ie} 10% 0.559<br>al£ 0072 D.103 0546 | 0.56<br>u<br>5<br>a 0.536 0.068 0.54 q<br>3=) s%o% 050 ou5<br>25<br>as 0.525 3<br>Log 0.526 0.92 9<br>5 a 0% l I - _ Hiest | l 05 S<br>uw @ yo a AN ah No a> od oh oD OY oh OD YD :<br>o O ad NS Sy a as we ay a ae a tb<br>ef 1 SHH<br>Gh HP Hg sg Pe Www gas<br>4 aE<br>aT -o'o 5<br>Aou 0.46 2=)<br>S<br>z<br>10%<br>Z 0.44<br>0.42<br><!-- End of picture text -->

-15% Ma@@additions (hs) mamdeletions (hs) — third moment (lhs) standard deviation (rhs)

<!-- Start of picture text --> 0.4<br><!-- End of picture text -->
hold spent a non-zero amount on items from that category, and 0 otherwise. The items represent goods that are more likely to be dropped from (included in) a household’s consumption basket when the household is subjected to negative (positive) income shocks, thereby improving the model’s ability to capture temporal changes in economic conditions. Figure 6 in Appendix 2.1 examines the evolution of premium good consumption in CPHS overtime.

# _Implementation_

The consumption model is estimated using data from the NSS and then applied to impute NSS-type consumption into the CPHS. Success of this approach is contingent on: (a) model stability (i.e., the model estimated in 2011 continues to apply in the years for which the CPHS is available), (b) sufficient predictive power of the model (i.e., the predictors are sufficiently correlated with household consumption), and that (c) the predictors are consistently measured between the two surveys. The analysis presented in section 3 confirms that the levels and trends in demographics, education and asset ownership observed in the (reweighted) CPHS are consistent with those observed in the nationally representative benchmark surveys.<sup>22</sup> The regression model, estimated separately for urban and rural India, is shown in Table 2 (the coefficients related to principal industry of occupation is suppressed for formatting purposes). The urban model fits the data better when compared to the rural model, which is consistent with consumption models estimated to data from other countries (e.g. Douidich, et al., 2016). Overall, families with higher share of dependents (members below the ages of 18 and above the age of 61) are associated with lower consumption per capita, while households with more educated members and greater ownership of assets are associated with higher per capita consumption.

|**Dependent variable:** Log consumption per capita|(1)<br>Rural|(1)<br>Urban|
|---|---|---|
|1-member household|0.74***|0.99***|
||(38.10)|(56.03)|
|2-member household|0.53***|0.64***|
||(46.90)|(47.17)|

> 22Figure 7 of the Appendix 2.2 shows the share of principal industry codes of households are also consistent across NSS-2011 and CPHS. Share of households with agriculture as the principal industry code are excluded in the graph for ease of representation: 39.1 percent of households in NSS-2011 and 33.1 percent of households (averaged across years) in CPHS belong to this category. In NSS-2011, principal industry code refers to the industry from which the households obtained their maximum income. In CPHS, we construct this variable based on the industry code of the household head. Households with missing principal industry code (due to head of household being unemployed or no member of the household being active in the labor market) are set to zero.

28
|3-member household|0.37***|0.45***|
|---|---|---|
||(45.73)|(46.13)|
|4-member household|0.24***|0.29***|
||(38.64)|(38.89)|
|5-member household|0.12***|0.14***|
||(22.63)|(20.35)|
|Multigeneration family|-0.00|0.01|
||(-0.94)|(1.29)|
|Extended family|0.03***|0.06***|
||(3.90)|(7.59)|
|Share of 0 to 18 years old members in family|-0.18***|-0.22***|
||(-21.21)|(-20.27)|
|Share of 61+ years old members in family|-0.04*|-0.03|
||(-2.34)|(-1.50)|
|Female headed households|-0.04***|-0.04***|
||(-6.12)|(-5.24)|
|Log (age of household head)|0.03***|-0.02|
||(3.34)|(-1.71)|
|Any member with higher than middle to high school level of education|0.02***<br>(3.41)|0.03**<br>(2.98)|
|Share of members with middle to high school level of education|0.12***|0.13***|
||(12.49)|(10.95)|
|Any member with diploma to post graduate level of education|0.05***|0.05***|
||(7.87)|(8.10)|
|Muslim household|0.03***|-0.02*|
||(5.18)|(-2.29)|
|Christian household|0.09***|0.03*|
||(5.54)|(2.05)|
|Sikh household|0.14***|0.03|
||(9.41)|(1.50)|
|Jain household|0.07|-0.01|
||(1.03)|(-0.26)|
|Buddhist household|-0.03|0.04|
||(-1.07)|(1.75)|
|Zoroastrian and other religions|-0.07|0.07|
||(-1.40)|(1.00)|

29
|Scheduled Castes|0.09***|0.01|
|---|---|---|
||(12.09)|(0.63)|
|Other Backward Classes|0.16***|0.05***|
||(23.47)|(3.77)|
|Other castes|0.19***|0.12***|
||(24.93)|(8.82)|
|Electrifed household|0.11***|0.15***|
||(21.47)|(10.98)|
|Rented household|0.22***|0.25***|
||(14.25)|(28.61)|
|Television owning household|0.17***|0.16***|
||(35.56)|(19.77)|
|Air conditioner owning household|0.08***|0.05***|
||(9.55)|(8.00)|
|Washing machine owning household|0.08***|0.17***|
||(6.33)|(23.99)|
|Refrigerator owning household|0.24***|0.23***|
||(32.50)|(37.41)|
|Car owning household|0.15***|0.30***|
||(12.11)|(32.03)|
|Computer owning household|0.23***|0.25***|
||(14.37)|(32.63)|
|Household owns the homestead|-0.00|0.00|
||(-0.33)|(0.19)|
|Inverter owning household|0.13***|0.05***|
||(9.67)|(5.57)|
|Dummy for Clothing, footwear, accessories|0.20***|0.14***|
||(48.27)|(29.96)|
|Dummy for Books, newspapers, stationery, tuition, hobbies|0.08***|0.13***|
||(20.68)|(23.83)|
|Dummy for Furniture and fxtures|0.24***|0.24***|
||(29.90)|(20.71)|
|Dummy for Cooking and household appliances|0.13***|0.12***|
||(14.78)|(15.01)|
|Constant|6.17***|6.46***|
||(171.10)|(134.87)|

30
|Observations|41,915|31,923|
|---|---|---|
|R-squared|0.4674|0.6314|

Table 2: Regression coefficients from the imputation model. Notes: Standard errors in parentheses.<sup>*</sup> _p<_ 0.05,<sup>**</sup> _p <_ 0.01,<sup>***</sup> _p <_ 0.001. Regressions are weighted by person level weights from respective surveys. Coefficients of harmonized industry codes are suppressed to keep the results tractable. The regression coefficients reported are based on a set of districts common between NSS-2011 and CPHS’ 2015. As CPHS expanded to a few more districts in the following years, the set districts common to the two surveys expanded slightly resulting in slightly different regression coefficients across years.

The error term from the regression model is accounted for when imputing NSS-type consumption into the CPHS. Given the non-normality observed in the NSS, we follow Elbers, et al. (2003) by drawing the errors from the empirical residuals with equal probability (to preserve the empirical distribution for the errors observed in the NSS). Errors terms for households in the CPHS are standardized using the mean and standard deviation, multiplied by the root mean square error term and added to the predictions of the imputation model into CPHS.

Figure 13 compares the mean, variance, and third moments of the imputed (log) NSS-type consumption into the CPHS to the moments of observed (log) consumption from both the NSS and the CPHS. The means of imputed NSS-type consumption and observed CPHS consumption are nearly identical in rural areas. In urban areas, NSStype consumption is on average approximately ten percentage points higher when compared to observed CPHS consumption. This suggests that the CPHS under-estimates consumption in urban India (consistent with observations made in Dhingra and Ghatak, 2021).

The variance of the imputed NSS-type consumption is seen to match the variance of observed NSS-2011 consumption in both rural and urban India, i.e. the use of imputed consumption and adjusted CPHS weights fully closes the gap in variance between the two surveys. Unfortunately, this does not extend to higher moments. While the use of imputed NSS-type consumption in the CPHS helps reduce the gap in third moments (compared to observed log consumption in the NSS), the remaining gap is economically significant and will bias estimates of poverty and inequality if not addressed. This motivates our second approach which is outlined next.

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<!-- Start of picture text --> 78<br>—NSS-type consumption — Reported CPHS consumption<br>76 as<br>7 a<br>12 _7~<br>68<br>66<br>?SSs> => SF=> FS> => SScS> eS> SFRS> SSRS> RSS<br>= OS sx swa s» Sea o Sa Ssoe So~<br><!-- End of picture text --> <!-- Start of picture text --> 05<br>—Repoted CPHS —NSS-type === NSS-2011<br>0.45os oe<br>0.35<br>03<br>02<br>$aoySs»> DSwg/§> DS 4§ $»/§ $* A » BSNo>eXBSwe> BSx“»eSBS&» BSY»SF<br><!-- End of picture text --> <!-- Start of picture text --> 02<br>0.16<br>0.12<br>0.08 Ne \<br>0.04 ~~<br>0<br>> 2. 2 2 SS GS oe oS<br>aofs wgJs 4s »SsoS* A No»eewe> x“s &s Y»<br>»v + v v > S os > S ~~<br>— Reported CPHS ——NSS-type --- NSS-2011<br><!-- End of picture text -->
# **4.2 Approach 2**

## _Model_

Approach 2 uses a single predictor to impute NSS-type consumption into the CPHS, namely observed CPHS consumption, a variable that is arguably highly predictive of NSS-type consumption, but which is entirely ignored in approach 1. In other words, in this approach we will convert the observed CPHS consumption into NSS-type consumption. Let CPHS-consumption expenditure for household _i_ be denoted by _xi_ . Section 3.2 establishes the following stylized facts: (a) The variance of NSS log consumption is higher than the variance of CPHS log consumption. The re-calibration of the survey weights has reduced this gap in the second moment, but some gap still remains, and (b) CPHS log-consumption is near normally distributed, while NSS log consumption shows a more marked deviation from normality. Specifically, the third moment of NSS log consumption is approximately twice the third moment of CPHS log consumption. (A similar ordering applies to the fourth moment.) To accommodates the above-mentioned stylized facts, consider a model where CPHS log consumption is described as a linear combination of NSS log consumption and a normally distributed error term: where _εi_ is an independent identically distributed error term with mean zero and unit variance. In practice we do not observe _yi_ and _xi_ for the same household _i_ given that the two measures of consumption come from different cross-sectional surveys with their own samples of households that cannot be linked. Accordingly, the model that describes the relationship between the two cannot be estimated using standard regression analysis (which is the reason why observed CPHS consumption was excluded as a predictor in approach 1). Instead, the parameters _a_ , _b_ , and _σ_ will be estimated using method of moments.

A minimum of three moment conditions will be required. The first three moments of the log consumption distribution are natural candidates. The mean and variance of both sides of eq. (2) solve: where _μq_ and _σq_<sup>2evaluate the mean and variance of the variable</sup><sup>_q_,respectively.At this</sup> point we have two moment conditions and three unknown parameters, meaning that a 33
third moment condition is required to obtain identification. For the third moment, we obtain: The first two moments do not require any assumption about the distributional form of _ε_ . Identification through the third moment, however, rests on the non-normality of the log consumption distributions.

**Assumption 1** _Assume that εi is normally distributed, and that_ log _xi and_ log _yi are non-normally distributed._

Under Assumption 1, we have _E_ [ _ε_<sup>3</sup> _i_<sup>]=0,while</sup><sup>_E_[(log</sup><sup>_yi−μy_)3]and</sup><sup>_E_[(log</sup><sup>_xi−μx_)3]</sup> are presumably non-zero. It is furthermore assumed that _εi_ is uncorrelated with log _xi_ . This similarly opens the door for identification. It follows that: since _E_ [(log _yi − μy_ )] = _E_ [ _ε_<sup>3</sup> _i_<sup>] = 0.Thisyieldsthefollowingestimatorfor</sup><sup>_b_:</sup> Note that identification fails when log incomes are normally distributed, in which case _E_ [(log _yi − μy_ )<sup>3</sup> ] = _E_ [(log _xi − μx_ )<sup>3</sup> ] = 0. Given the estimate for _b_ , estimates of _a_ and _σ_<sup>2</sup> can be obtained by solving equations (3) and (4): It will be convenient to re-arrange the model as follows: Given estimates for _a_ , _b_ , and _σ_ , we can treat log ̃ _xi_ as observed data.

The next challenge is to extract a drawing for log _yi_ given an observed value for log ̃ _xi_ . To this end, we assume that the distribution for log _yi_ can be described by a normal mixture distribution. Let the cumulative distribution function for NSS log 34
consumption be denoted by _Fy_ .

**Assumption 2** _Fy can be represented by a normal mixture distribution of the form:_

_where Fj are normal distribution functions with mean mj and variance s_<sup>2</sup> _j_<sup>_,andwhere_</sup> _πj are non-negative mixing probabilities that sum up to_ 1 _._ Under Assumption 2, the distribution for log ̃ _xi_ denoted by _Gx_ can also be represented by a normal mixture distribution. It follows that: where _Gj_ are normal distribution functions with mean _mj_ and variance _νj_ = _s_<sup>2</sup> _j_<sup>+</sup><sup>_σ_2</sup><sup>_/b_2.</sup> Since log ̃ _xi_ is observed, the normal mixture distribution _Gx_ can readily be estimated (see for example the FMM package in Stata). This gives us estimates for _πj_ , _mj_ and _νj_ . Note that this also identifies two-thirds of the parameters of _Fy_ (as the parameters _πj_ and _mj_ are shared between _Fy_ and _Gx_ ). To fully identify _Fy_ , we also need estimates for _s_<sup>2</sup> _j_<sup>,whichcanbeobtainedbycombiningestimatesfor</sup><sup>_νj_withtheestimatesfor</sup><sup>_σ_2</sup> and _b_ , as: _s_<sup>2</sup> _j_<sup>=</sup><sup>_νj−σ_2</sup><sup>_/b_2(providedthat</sup><sup>_νj>σ_2</sup><sup>_/b_2;ifthisconditionisviolated,we</sup> could reduce the number of components by one until all mixture components satisfy this condition).

At this point we have an estimate of the unconditional distribution _Fy_ for NSS log consumption log _yi_ . What we really want is an estimate of the distribution for log _yi_ conditional on the observation of CPHS log consumption log ̃ _xi_ for household _i_ . Let us denote this conditional distribution by _Fy|x_ . It follows that _Fy|x_ is also a normal mixture distribution (see e.g. Elbers and van der Weide, 2014), i.e. _Fy|x_ satisfies _Fy|x_ =<sup>�</sup> _j_<sup>_αjFj|x_,where</sup><sup>_Fj|x_are normal distribution functions with mean</sup><sup>_mj|x_</sup> and variance _s_<sup>2Lemma2fromElbersandvanderWeide(2014)showsthatthe</sup> _j|x_<sup>.</sup> parameters that define _Fy|x_ can be derived from the parameters of the normal mixture ̃ _Fy_ and the estimate for _σ_<sup>2</sup> = _σ_<sup>2</sup> _/b_<sup>2</sup> :

35
with: where _φ_ ( _x_ ; _m, v_ ) is a normal density function with mean _m_ and variance _v_ evaluated at ̃ the value _x_ . Note that when the variance of the error term tends to zero (i.e. _σ_<sup>2</sup> _→_ 0), the conditional mean _E_ [log _yi|_ log ̃ _xi_ ] will tend to log ̃ _xi_ while the conditional variance will tend to zero, as they should.

A practical way to proceed is to draw an observation of NSS log consumption from the conditional distribution _Fy|x_ for each household, and evaluate the welfare measures of interest. We draw 50 observations of NSS-type log consumption for each household in the CPHS sample, and then compute the aggregate welfare indicator (i.e. poverty and inequality) for each _k_ = 1 _, . . . ,_ 50. The mean and standard deviation evaluated over the _K_ realizations will serve as the point estimate and standard error of the welfare indicator.

Alternatively, when measuring head-count poverty for example, one could evaluate for each household the probability that their NSS log consumption is below the poverty line conditional on the observation of their CPHS log consumption value -- and then compute the mean value of these probabilities across all households in the sample. Let the poverty line for log consumption be denoted by _z_ . The probability that household _i_ is poor equals: where Φ is the standard normal distribution function. Head-count poverty can then be estimated by: where _wi_ denote survey weights that are assumed to sum up to 1.

# _Implementation_

The assumed model (see eq. 2) contains three parameters: _a_ , _b_ , and _σ_<sup>2</sup> . As described above, a minimum of three moments (for both the NSS and CPHS log consumption data) are required to estimate all three of these parameters. All three moments of the CPHS log consumption distribution can readily be estimated using the observed CPHS consumption data. Estimation of the moments from the NSS consumption distributed is complicated by the fact that there is no NSS survey for the same moment in time for which we have CPHS. We have established however that the third moment of NSS 36
consumption is remarkably stable over time, allowing us to use the third moment estimated to observed NSS consumption from the NSS-2011. For the second moment, we consider two options, namely estimate it using (a) observed NSS consumption data from the NSS-2011, and (b) imputed NSS-type consumption in the CPHS (which we established does reasonably well in matching the second moment from the observed NSS log consumption data). The first moment (mean log consumption), which is the least stable moment over time, is obtained from the imputed NSS-type consumption data. The resulting estimates of the three parameters _a_ , _b_ , and _σ_<sup>2</sup> for the different years are shown in Figure 14.

The next step is to estimate the parameters of the unconditional distribution of NSS log consumption, which is assumed to follow a Normal Mixture distribution. Normal mixtures (NM) are very flexible. Two or three components are generally sufficient to closely fit any empirical distribution function underlying household consumption data.<sup>23</sup> In our case, it offers two practical advantages. First, it follows that the distribution of NSS log consumption conditional on CPHS log consumption too follows a NM distribution. Second, the parameters of the NMs associated with both the unconditional and conditional distribution of NSS log consumption can readily be derived from the parameters of the NM estimated to CPHS log consumption combined with the parameters governing the relationship between CPHS and NSS consumption (i.e. _a_ , _b_ , and _σ_<sup>2</sup> ).

We start by fitting a NM with three components for the unconditional NSS log consumption distribution. When the estimated variance of one or more of the components is negative, the number of components is reduced by one, until all components are estimated to have positive variance. See assumption 2 for details on the positive variance constraint (and why positive variance is not necessarily guaranteed). Negative variance estimates are only obtained for urban samples during 2018.

Once we have an estimate of the conditional distribution, we obtain 50 random draws of NSS consumption for each household in the CPHS sample (conditional on each household’s CPHS consumption value). For each of the 50 realizations of NSS consumption data, we evaluate the corresponding poverty headcount rates and selected measures of inequality. The point estimates of poverty and inequality are obtained by averaging over the 50 different realizations.

When a new NSS household consumption survey becomes available, both NSSconsumption and CPHS-consumption can be observed for the same year (albeit in different surveys with their own sample of households). Accordingly, one could estimate

> 23To illustrate, we report the empirical goodness of fit for the mixed normal distributions for the years 2015 and 2019 in Figure 8 of Appendix 3.1

37
all three moments of NSS log consumption using the observed data and adopt our method of moments estimator to obtain estimates of _a_ , _b_ , and _σ_<sup>2</sup> for that year -- and subsequently assume that all three parameters remain constant over time until the next NSS household consumption survey becomes available (which is when the first three moments derived from observed consumption data can be updated). Alternatively, one could continue to adopt the version of Approach 2 we are currently using, namely estimate moments that are found to be comparatively stable over time from observed household (log) consumption data and estimate moments that are found to be less stable from up-to-date imputed consumption data. The latter (and currently adopted) approach may be preferred when the CPHS sample is subjected to notable changes that may significant introduce changes in moments that are not accounted for by reweighting. See Appendix 3.3 for a further discussion on the changes made to the CPHS sample (most notably during the third wave of 2017) and its implication for our method of estimation.

On the choice between Approaches 1 and 2, it should be noted that the two approaches rely on their own set of assumptions. The validity of these assumptions will be context-specific and may vary over time. Approach 1 assumes that the relationship between NSS-consumption and household characteristics such as demographics, education, and employment is stable over time, while Approach 2 assumes that the relationship between NSS-consumption and CPHS-consumption is stable over time. Where possible one should implement both approaches (thereby considering different assumptions) and inspect robustness. Appendix 3.2 compares the relative ranking of households based on their observed CPHS consumption and imputed consumption based on approach 1 of section 4.1 and approach 2 of section 4.2.

# **5 Results**

## **5.1 Main estimates of poverty and inequality**

Both approaches yield qualitatively similar levels and trends in headcount poverty estimated at the $1.90 line: poverty is about 12.3 percentage points lower in 2019 than 2011 (see Figure 15). Estimates of poverty obtained using observed CPHS consumption data are seen to be up to 3.5 percentage points higher when compared to estimates obtained using NSS-compatible measures of consumption. By the same token, our estimates of poverty are notably higher than previous estimates obtained by the World Bank’s Povcalnet database and other scholars, see e.g. Edochie, et al. (2022); Newhouse and Vyas (2019) and Gupta, Malani and Woda (2021b). Estimates from World Bank’s 38
Povcalnet are included in Figure 15 for comparison. The projections in Povcalnet are extrapolated using the consumption distribution of NSS-2011 and applying the growth in private final consumption expenditure observed in national accounts. The method therefore assumes that inequality has remained unchanged since the NSS-2011<sup>24</sup> . We compare our approach to Newhouse and Vyas (2019) and Edochie, et al.(2022) in Section 5.2 and reflect on the potential reasons for why their estimates are lower. Gupta, Malani and Woda (2021b) use the raw CPHS data to construct headcounts for 2019 and the post-pandemic period; our reservations with this approach are documented in Section 3.

The rate of poverty reduction between 2004 and 2011 is estimated at approximately 2.5 percentage points per year. After 2011 poverty reduction has slowed down. By our estimates, poverty has declined by an average of 1.3 percentage points per year between 2011 and 2018. It should be noted that at lower levels of poverty, it would take increasingly larger rates of consumption growth and/or reductions in inequality to sustain the high rates of poverty reduction (e.g. Bourguignon, 2003).

Figure 12 in Appendix 4.1 dis-aggregates the trends in poverty by rural and urban. Three observations stand out. First, rural poverty in 2019 is 14.7 percentage points lower than in 2011 while urban poverty reduced by 7.3 points over the same period. This is consistent with a continuation of the rural-urban poverty convergence observed over the past six decades (see Datt, Ravallion and Murgai, 2019).<sup>25</sup> Second, urban India experienced a churn in poverty trends around 2016. Urban poverty rose by 2 percentage points in that year followed by a rapid rise in consumption that drove poverty down by 3.2 percentage points in the following year. Third, the fastest poverty reduction occurred in the years 2017 and 2018. Thereafter, the rate of poverty reduction stalled considerably.

Headcount poverty rates at the international $3.2 and $5.5 poverty lines are shown in Figure 13 of Appendix 4.2. A similar reduction in poverty is observed for both lines. The average rate of poverty reduction at $3.2 and $5.5 was 2.1 and 0.8 percentage points per year between 2004 and 2011. By comparison, all years since 2015 clock an average rate of 1.2 and 0.6 percentage points poverty reduction per year relative 2011. The $5.5 line also shows poverty rising between 2018 and 2019. This dynamic is detected in the consumption data but not by changes in demographic and asset levels. The rise is mainly on account of urban households where headcount rates rose by 2.5 percentage 24Povcalnet projections can allow for some changes to the distribution. For instance, the 2014.5 estimate employs a pass-through rate of 0.559 for urban and 0.733 for rural areas; see box 1.3 in World Bank (2018) and box 1.2 in World Bank (2020) for details. However, the distribution within rural and urban areas is assumed to be unchanged.

> 25Note that rural poverty reduction in the decade(s) prior to 2004 was more modest and heterogeneous, see e.g. Lanjouw and Murgai (2009) and Himanshu et al. (2013).

39
in that year.

Let us also inspect time-trends in inequality. Figure 16 shows our estimates of the Gini coefficient for the years under consideration. Both approaches are found to produce qualitatively similar results.<sup>26</sup> We observe a slight moderation in consumption inequality in India since 2011. This could in part be attributed to the fact that top-income households are under-represented in household surveys (whether NSS or CPHS). Consequently, consumption inequality estimated from household survey data capture distributional changes for households that are in the bottom 95 percent, say, of the distribution. To the extent that the income or consumption growth since 2011 is largely concentrated in the top end of the distribution (Chancel and Piketty, 2019), our household survey-based estimates of consumption inequality will be downward biased.

Figure 14 in Appendix 4.3 reveals that the moderation of inequality has been larger in rural than urban areas. Since 2015, changes in rural inequality have been less pronounced than urban areas. Urban inequality dropped in 2018 which coincides with the year in which the rate of poverty reduction was its highest. Figure 15 in Appendix 4.4 shows that other measures, namely, poverty gap and mean-log deviation yield trends in poverty and inequality dynamics that are consistent with the main results.

Finally, in Figure 17, we connect our estimates of poverty and inequality for India over the last decade with estimates dating back to 1993. It can be seen that our estimates of headcount poverty preserve the long-term trend of poverty reduction that is observed in India over this period. By the same token, our estimates suggest that the current poverty rate is higher than the forecasts based on pass-through adjusted consumption growth from national accounts (under the assumption of distribution neutrality). For consumption inequality we observe a trend reversal around 2011 (see Figure 18). Inequality is estimated to have steadily increased between 1993 and 2011. By our estimates inequality has started to moderate after 2011.

# **5.2 Robustness analysis**

Our preferred specification in approach 2 assumes a linear relationship between observed CPHS consumption and NSS consumption. We allow for heterogeneity (i.e. different relationships) between urban and rural India. It is possible however, that there are additional heterogeneities that should be accounted for. For instance, Gibson and Kim (2007) observe that the measurement errors in household consumption are systematically correlated with household size. Similarly, Beegle, et al. (2012) find that

> 26The inequality based on reported CPHS consumption range between 0.2965 and 0.3213 across years (not included in the figure) -- considerably lower than the estimates of inequality obtained using NSS-type consumption measures.

40
in addition to household size, the number of adults in the household, the education level of the household head and asset ownership levels can induce systematic differences between different measures of household consumption.

To test whether any potentially important heterogeneities are overlooked by our preferred specification, we allow the linear relationship between CPHS and NSS consumption to vary by these household characteristics. We consider six binary household level indicators: households with more than three adults, households with at least one member with a high level of education, household head with over primary levels of education, households with agriculture as the primary industry, Hindu households, and households that belong to schedule caste, schedule tribe or other backward classes. Each of these will be combined with the rural-urban indicator, such that four different linear relationship are estimated for each of these six cases.

Figure 19 plots the headcount poverty rate at the $1.90 line for each of the six specifications -- each accounting for a different choice of heterogeneity (labeled as the “heterogeneous” series). The “homogenous” series refers to our main specification that only accounts for heterogeneity between rural and urban India. All six specifications, each accounting for a different form of heterogeneity, produces similar levels and trends in headcount poverty than the estimates obtained with our preferred specification. The one outlier is the headcount estimate obtained for 2018 that accounts for heterogeneity in household head literacy.

We can further check the robustness of our imputation model of approach 1 by estimating poverty in 2004 and comparing it to the actual estimates for the year. This “back casting” exercise generates poverty figures for 2004 based on the estimated coefficients in Table 2 and imputing consumption for 2004 based on the NSS consumption round for the year. The back casted estimates can also help compare our approach to those of Newhouse and Vyas (2019) and Edochie, et al. (2022). As all three papers use the same training and validation dataset (NSS-2011 and 2004 respectively), these comparisons can reveal the accuracy of prediction across papers.

41
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In Figure 20, we plot the gap between back casted poverty projections and the actual poverty rate for 2004 across studies. Estimates closer to the horizontal axis show that the predicted poverty rates were close to the actual rate observed in 2004. The graph shows that approach 1 of our study predicts 2004 poverty rate to be 3.4 percentage points lower than the actual headcount across India and 3.2 percentage points lower rate for urban samples.<sup>27</sup> In comparison, estimates from Newhouse and Vyas (2019) are 2.2 percentage point apart from the actual national rate but the differences for urban samples are 9.2 percentage points higher. Deviations from the actual poverty rate in Edochie, et al. (2022) are in the same direction as our estimates but the magnitude is considerably higher in their study across all samples. Overall, these out-of-sample predictions for NSS-2004 suggest that our approach yield estimates that are closer to the actual headcount rate across rural, urban and all-India samples.

We believe that the inability to model changes in household asset ownership overtime could have led the earlier papers to overestimate poverty reduction in 2015 and 2017 and produce incompatible back casted estimates of poverty for 2004 (asset indicators were unavailable in the surveys used in the two papers). Our analysis in Section 6 using PLFS shows that asset indicators are important predictors of household consumption; failing to capture these indicators leads to divergent poverty estimates even within the same survey.

# **6 Corroborative evidence**

Our estimates of poverty are at odds with findings from the leaked NSS-2017 survey which shows a rise in poverty between 2011 and 2017. Both sources point to a moderation of inequality since 2011, but the magnitude of changes to inequality are significantly higher in the NSS-2017 relative to our estimates. In this section, we corroborate our main findings using a range of independent data sources.

## **6.1 Headcount poverty has declined after 2011 with larger reductions in rural areas**

**Estimated consumption levels sit well with private final consumption expenditure (PFCE) reported in national accounts** . A number of earlier studies have shown that there are systematic differences in consumption growth reported in national accounts statistics (NAS) and household surveys (see e.g. Ravallion, 2003; Datt

> 27Mean consumption per capita in the 2004 survey is 83.88 PPP dollars. The mean imputed 2004 consumption is 82.684 (1.4 percent lower than the survey mean).

47
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# **provides further confirmation that poverty in India is lower in 2017 than in**

**2011** . Consumption trends in past rounds of the IHDS and NSS surveys have tracked each other closely -- both surveys were conducted in 2004 and 2011 and predicted comparable drops in extreme poverty over this period. A limitation of IHDS-3 is that it is limited to the states of Bihar, Rajasthan and Uttarakhand. For this validation exercise therefore, we restrict the CPHS sample to these three states.

The IHDS captures consumption using the mixed recall period whereas the CPHS consumption used in our analysis corresponds more closely to the uniform recall period. Furthermore, IHDS-3 consumption values reported in Desai (2020) are in constant 2017 values and deflated using the _monthly_ CPI-AL and CPI-IW series. The consumption values in our analysis are in constant 2011 terms deflated using _yearly_ CPI-AL and CPI-IW series. For these reasons, we will be comparing changes in real consumption across the two sources (rather than comparing levels).

Real consumption grew at an annualized rate of 2.7 percentage points between the IHDS 2011-12 and 2017. The average annualized consumption growth over the same period in our analysis (approach 2) is 1.5 percent.<sup>28</sup> Real consumption growth in the IHDS-3’s rural and urban samples are 3.8 and -0.7 percent per year. By comparison, consumption growth in rural and urban in our analysis is 1.7 percent and 0.6 percent, respectively. Both surveys therefore point to faster growth in rural areas than urban areas. The differences in consumption recall and deflators used in the two surveys could account for the difference in magnitudes of the observed growth rates.

Correlates of consumption, such as durable asset ownership, are similar across the two surveys. Thirty-two percent of households in the IHDS-3 states own motorcycles and cars and 21 percent possess air coolers and air conditioners. In the reweighted CPHS, ownership shares of these two assets are 34 and 22 percent, respectively. Growth in monetary and non-monetary indicators in the IHDS-3 therefore are consistent with the observation that poverty in 2017 is lower than in 2011.

**Another assessment of poverty since 2011 can be made by comparing rural headcounts to rural wages produced by India’s Labor Bureau.** Monthly wages for agricultural and non-agricultural occupations are available since 1998. We take a weighted average of wages across occupations to construct a composite monthly rural wages series. The series is then deflated using monthly CPI-AL series and collapsed at the yearly level by taking a simple average across months.

Figure 22 correlates the growth in average annual wages for rural workers with yearon-year changes in rural poverty headcounts from our analysis (approach 2). As real

> 28The average real consumption in NSS-2011 for the three states is 1259.01 (constant 2011 rupees). For rural and urban areas, the mean consumption in NSS-2011 is 1141.57 and 1885.60 respectively.

50
<!-- Start of picture text --> 4.0% 0.01<br>3.0%<br>3.0% f2°%fs, 0<br>Efo}<br>2.0% 1.7% o<br>% -0.01<br>4 B 2d 1.0% 1.0%,0807 agzg<br>4 eo<br>2 -1.9X0 -0.02 &<br>&,2 0.0%9.02 g8<br>g be}<br>5&-0.03a§<br>g<br>Fs -1.0% 2% og<br>z22” -0.04 §<br> 2.0% 2<br>ne<br>9<br>0.05 ”<br>-3.0% -0.05<br>-5.3% or0"<br>-4.0% -0.06<br>2015-16 2016-17 2017-18 2018-19 2019-20<br>—growth in average annual rural wages — Change in headcount rate<br><!-- End of picture text -->
into the CPHS (denoted by “CPHS-NSS”<sup>30</sup> ). Mean consumption per capita from the PLFS 2017 is estimated at Rs. 2385, which is approximately 7 percent higher than the NSS-2011 on an annualized basis. Note that these predictions rely only on changes in non-expenditure variables -- meaning that the growth of non-monetary predictors of consumption, as captured by the nationally representative official survey, must have been positive since 2011. This is further evidence that poverty in 2017 is lower than in 2011.

||20|17|20|18|20|19|
|---|---|---|---|---|---|---|
||**PLFS**|**CPHS**|**PLFS**|**CPHS**|**PLFS**|**CPHS**|
|**PLFS-NSS**|2385|-|2525|-|2712|-|
|**CPHS-NSS**|-|2557|-|2843|-|3139|
|**CPHS-NSS-PLFS**|2404|2443|2548|2539|2758|2803|

Table 3: Mean consumption per capita based on different imputation models and surveys.

Notes: Mean consumption values are deflated using CPI-AL and CPI-IW in rural and urban areas. The PLFS and NSS-2011 samples excludes states which are not included in CPHS. “PLFS-NSS” denotes consumption per capita based on an imputation model that uses variables that are common to PLFS and NSS-2011 (see footnote 28); “CPHS-NSS” denotes a model using a set of variables that are common between CPHS and NSS-2011 (see footnote 29); and, “CPHS-NSS-PLFS” denotes the model using variables common across all three surveys (see footnote 30).

Nevertheless, the first two rows in Table 3 underscore potential differences between the imputed consumptions into the CPHS and PLFS: Consumption imputed into the CPHS is about 7 to 16 percent higher than the PLFS. It should be noted, however, that the two consumption estimates are not a strict like-to-like comparison: the consumption imputed into the CPHS is based on demographic as well as asset variables, whereas imputations into the PLFS are based only on slower-moving demographic indicators (asset variables are unavailable in PLFS). To construct comparable vectors of imputed consumption across the surveys, we select a set of demographic indicators that are family; share of 0 to 18 years old members in family; share of 61+ years old members in family; female headed households; log (age of household head); any member with higher than middle to high school level of education; share of members with middle to high school level of education; any member with diploma to post graduate level of education; dummy variables for Muslim; Christian; Sikh; Jain; Buddhist; Zoroastrian and other religions; scheduled castes; other backward classes; other castes; principal industry code of the household; household type; any regular salaried member in the household; household size and an interaction between the two variables. For urban sample we also include a dummy for cities that had over a million population in the 2011 census.

> 30The list of variables used in imputation are the same as in Table 2 of the main text

52
<!-- Start of picture text --> 20%<br>16%<br>12%<br>8%<br>4%<br>. ee<br>2017 2018 2019<br>4%<br>— Using variables common between PLFS-NSS and CPHS-NSS<br>— Using variables common between all three surveys PLFS-CPHS-NSS<br><!-- End of picture text -->
<!-- Start of picture text --> 10.00%<br>8.00% 7.6%<br>6.80%<br>6.00%<br>4.19<br>4.00%<br>1.809<br>2.00%<br>0.00% 0.7%. -0.8%<br>som ——.--peer 59 ee cdweet -1.7%<br>-4.00%<br>2004-1993 2011-2004 2017-2011 2018-2017 2019-2018<br><!-- End of picture text --> — Casual wage growth ——Poverty reduction per year (NSS) --- Poverty reduction per year (NSS-2011/CPHS)
time lights data is obtained from Beyer, Jain and Sinha (2021). The authors obtained raw night-time lights data from VIIRS-DNB Cloud Free Monthly Composites (version 1) and corrected the raw data for outlier observations (averaging cells overtime and clustering areas based on the intensity of night-time lights). These corrections follow the approach advocated by Elvidge, et al. (2017). Values of night-time lights are reported in nanowatts per square kilometer. We collapse the monthly nighttime-lights aggregates from Beyer, Jain and Sinha (2021) to yearly levels before evaluating growth rates.

Nielsen’s surveys track sales of consumer goods through retail store level surveys, covering a network of mom-and-pop stores as well as modern retail stores in 52 cities and 2700 villages across India. The instrument collects quantities, prices and sale values of both branded and non-branded items. We use estimates of quarterly growth in store-level sale values from publicly available sources<sup>32</sup> . The quarterly growth values are aggregated at the yearly level by taking simple averages, see Figure 25.

Both night-time lights and Nielsen’s store-level surveys indicate welfare indicators peaked in 2017 and 2018. This period coincides with rapid rate of poverty reduction in our analysis. The sources also suggest a slowdown in 2016 and 2019 which further supports our finding that the rate of poverty reduction peaked in 2017-2018 and moderated in 2019.

# **6.3 A rise in urban poverty in 2016 followed by a rapid rise in consumption in 2017**

**Consumption growth trends from the IHDS-3 can help validate a break in poverty trends around 2016** . The break in poverty reduction around 2016 coincided with a rise in urban poverty in that year. Household consumption strongly rebounded thereafter. Households interviewed by the IHDS in February to April 2017 reported a negligible rise in consumption since 2011-12. In contrast, household consumption for interviews conducted between May to July 2017 is 5 percent higher than 2011 on an annualized basis. Consumption of the first cohort of households was plausibly affected by the demonetization of currency notes in November 2016 followed by rapid growth in consumption as the economy was remonetized. We observe similar trends in our analysis albeit with smaller magnitudes. Consumption growth for the first cohort of

32 List of all sources: http://bsmedia.business-standard.com/ ~~m~~ edia/bs/img/article/2016-08/ 09/full/1470687448-3888.jpg, https://www.nielsen.com/wp-content/uploads/sites/3/2019/04/indiaFMCG-growth-snapshot-q3-2018.pdf, https://images.assettype.com/afaqs/2020-01/200d87dc-162d41ae-8fde-299faec4927f/Q4 ~~2~~ 019 ~~F~~ MCG ~~F~~ inal ~~D~~ eck.pdf. Quantity growth for 4<sup>th</sup> quarter of 2016 was not available online. 2015-16 references the period starting the third quarter of CY2015 to the second quarter CY2016.

55
<!-- Start of picture text --> 12.00% 2.00%<br>1.00%<br>10.00%<br>& FI<br>e&<br>20.00% ¥<br>% sow =e<br>go" g<br>Zg<br>g-1.00%<br>¥ -0.8% &<br>2 6.00% 2<br>é 0.8% &<br>o -0.8% -2.00% S<br>° B<br>3 5 Zz<br>gq 4.00% -2.6% g<br>28 -3.00% °8£<br>3 Oo<br>2.00%<br>-4.00%<br>-4.7%<br>0.00% -5.00%<br>2015-16 2016-17 2017-18 2018-19 2019-20<br>—Sales growth (Nielsen) —-Growthin NIL —Poverty reduction per year<br><!-- End of picture text -->
# **6.4 No rise in consumption inequality since 2011, but indications of a rise in 2019**

**The unreleased NSS-2017 shows a moderation in inequality but the magnitude of the reduction is comparatively large.** Based on leaked NSS-2017 results, Subramanian (2019) estimates rural and urban consumption inequality to have reduced by 0.0291 and 0.0387 Gini points since 2011 (based on modified mixed reference period in both NSS rounds). The direction of changes to inequality between NSS-2011 and NSS-2017 agrees with our findings. Our results differ, however, on the magnitude of the inequality reduction. Based on our estimates, average inequality reduction since 2015 in rural- and urban-India are 0.0007 and 0.007 Gini points (using the uniform recall periods of NSS-2011).

In Figure 26, we put the inequality estimates in a global context. Data on inequality is obtained from World Development Indicators. Countries that report at least one estimate of the Gini coefficient between 2009-2013 (two years before and after NSS2011) and 2015-2019 (two years before and after NSS-2017) are included. We average the Gini coefficients for each of the two time-periods and evaluate the difference in mean values to observe how much inequality has changed between the two points in time across countries. The MMRP-2011 level of Gini and the change in inequality based on NSS-2017 data is highlighted in blue; whereas the URP-2011 level of Gini and the change in inequality from our analysis is highlighted in red. It follows that there are only a handful of countries that report inequality reductions that are comparable to what is reported between the NSS-2011 and NSS-2017. By comparison, the rate of reduction based on URP-2011 and our analysis is found to sit well with global trends.

**Quintile consumption growth estimates in IHDS-3 show higher consumption growth in the bottom parts of the distribution** . Figure 27 compares quintile consumption growth rates from the IHDS-3 to our estimates. Average consumption growth in the bottom quintile of the distribution is higher than the growth rates observed for households at the top end of the distribution in both sources. These patterns are consistent with the observed moderation in consumption inequality. Desai (2020) finds that the Gini measure of inequality has fallen by 0.023 points between 2011-12 and 2017. Over the same period, inequality based on our estimates fell by 0.07 Gini points.

**NSS’ All-India Debt and Investment Surveys (AIDIS) show that wealth inequality too has fallen** . Using past rounds of NSS’ All-India Debt and Investment Surveys (AIDIS), Himanshu (2019) shows that gross wealth inequality increased by 0.01 and 0.08 Gini points between 1991-2002 and 2002-2012. The direction of changes

57
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0.9 <!-- Start of picture text --> 08 0.77<br>07 0.69 0.678<br>0.615<br>0.6<br>05<br>04<br>03<br>0.2<br>0.1<br>0<br>Rural Urban<br>m2013 2018<br><!-- End of picture text -->
<!-- Start of picture text --> 0.55<br>0.502<br>0.5<br>04845 0.436<br>42 0.424<br>04<br>0.369<br>0.351. 0.348 0337<br>0.33<br>0.3<br>EUS 2011 PLFS 2017 PLFS 2018 PLFS 2019<br>—rral —urban<br>8.0%<br>6.0%<br>4.0%<br>ne -. SSS<br>--s<br>mown “SsssSY<br>2.0% waSS.“Ssse<br>an<br>0.0%<br>2017-2011 204-2017 2019-2018<br>wetue msems<br>-2.0% -" aw<br>ae ss.<br>-"<br>-4.0%<br>——Salariedirural 9 --=Salariedurban 9 ——Casual,rural --=- Casual,urban<br><!-- End of picture text -->
<!-- Start of picture text --> 12.00% 35%<br>30%<br>10.00%<br>e3<br>25% 2<br>xy<br>»v 8.00% band°<br>8éQ3 20% zSs“4 g<br>= 6.00% 8<br>a oy<br>a 15% §<br>Ba<br>8wa<br>S °<br>4.00% &<br>10% &3<br>g<br>é<br>2.00% 5%-<br>0.00% 0%<br><O0.0lha. 0.01-04ha. 04-1 ha 1-2 ha 2-4 ha. 4-10 ha. 10+ ha<br>Percentage of poor per land-holding size — Real income growth<br><!-- End of picture text -->
A new household consumption survey was introduced in 2014, the Consumer Pyramid Household Survey (CPHS), collected by the private data collection company called the Center for Monitoring Indian Economy (CMIE). This is the first time since the NSS-2011 there is household consumption expenditure data to work with, opening new doors for the measurement of poverty and inequality in India. There are two limitations of the CPHS however that have to be addressed. The first is that the survey in its current form is not nationally representative (see e.g. the biases documented in Somanchi, 2021). The second is that it uses its own measure of consumption expenditure that is not readily comparable to the NSS measure of consumption.

This paper makes a comprehensive effort to address both of the above-mentioned concerns. We implement a rigorous reweighting exercise using multiple nationally representative benchmark surveys to obtain adjusted sampling weights that make the CPHS nationally representative. The adjusted weights will be put in the public domain and hopefully serve as a public good to anyone looking to use the CPHS. We address the second concern by estimating the relationship between CPHS- and NSS-consumption and using this to impute NSS-type consumption directly into the CPHS. This allows us to compare our estimates of poverty to the official estimates for 2011, and by extension evaluate how poverty and inequality have evolved over the last decade.

We find that extreme poverty in India has declined by 12.3 percentage points between 2011 and 2019 but at a rate that is significantly lower than observed over the 2004-2011 period. Poverty reduction rates in rural areas are higher than in urban areas. We detect two incidences of rising poverty in our period of analysis: urban poverty rose by 2 percentage points in 2016 during the demonetization event and fell sharply thereafter; and, rural poverty rose by 10 basis points in 2019 likely due to a growth slowdown. Our estimates of poverty for recent periods are more conservative than earlier projections based on consumption growth in national accounts and other survey data. Finally, we do not find evidence of rising consumption inequality in our analysis. Our findings are supported by a comprehensive set of independent data sources.

The approach we developed to convert CPHS consumption into NSS consumption could be used to monitor poverty between the NSS years, thereby increasing the frequency of India’s poverty estimates. The approach may also find use outside of India. The first-best approach of course is to work with actual up-to-date household consumption expenditure data. Any imputation-based estimates of poverty and inequality are inferior to survey-direct estimates that are obtained from observed household consumption data. Imputation methods are necessitated when real up-to-date household consumption data are not available. When the imputation methods considered in our study are used to estimate poverty and inequality for the years in between NSS rounds, 63
the precision of these estimates is increased when the gaps in time that need to be bridged are reduced (i.e. when the frequency of NSS surveys is increased) -- as the assumptions underlying the imputation methods come under increasing pressure when the most recent household consumption survey becomes increasingly outdated.

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