metadata: authors: 0: author: Castaneda, R. Andres
1: author: Caruso,German Daniel
2: author: Malasquez,Eduardo
3: author: Lucchetti,Leonardo Ramiro
4: author: Scot,Thiago
count: Latin America,Caribbean
docna: 0: docna: But … what is the poverty rate today?
            testing poverty nowcasting methods in Latin America and the Caribbean
docty: Policy Research Working Paper
subtopic: Labor & Employment Law,Poverty Impact Evaluation,Poverty Monitoring & Analysis,Poverty Reduction Strategies,Inequality,Poverty Assessment,Poverty Diagnostics,Poverty Lines,Small Area Estimation Poverty Mapping
teratopic: Poverty Reduction
abstracts: cdata!: Poverty estimates usually lag behind two
            years, which makes it difficult to provide real-time poverty
            analysis to assess the impact of economic crisis and shocks
            among the less well-off, and subsequently limits policy
            responses. This paper takes advantage of up-to-date average
            economic welfare indicators like the gross domestic product
            per capita and comprehensive harmonized micro data of more
            than 180 household surveys in 15 Latin American countries.
            The paper tests three commonly used poverty nowcasting
            methods and ranks their performance by comparing
            country-specific and regional poverty nowcasts with actual
            poverty estimates for 2003–14 period. The validation results
            show that the two bottom-up approaches, which simulate the
            performance of each agent in the economy to nowcast overall
            poverty, perform relatively better than the top-down
            approach, which uses welfare estimates to explain the
            performance of poverty at an aggregate level over time. The
            results are robust to additional sensitivity and robustness tests.
repnme: repnme: But … what is the poverty rate today?
            testing poverty nowcasting methods in Latin America and the Caribbean
display_title: But … what is the poverty rate today
            testing poverty nowcasting methods in Latin America and the Caribbean
listing_relative_url: /research/2017/06/27643265/…-poverty-rate-today-testing-poverty-nowcasting-methods-latin-america-caribbean
topicv3: Poverty m1326687 695,Poverty Measurement and Analysis m1326941 707,Population, Aging and Health m1327736 640,Income Inequality m1503891 2668,Household Surveys m1504071 2761
publishtoextweb_dt: 2017-06-19T00:00:00Z
historic_topic: Poverty Reduction
no_of_pages: 36
author_keys: 0: author_key: 995905
1: author_key: 763344
model_extractions: WPS8104 Policy Research Working Paper 8104 But ...What Is The Poverty Rate Today?

Testing Poverty Nowcasting Methods in Latin America and the Caribbean _German Caruso Leonardo Lucchetti Eduardo Malasquez Thiago Scot R. Andrés Castañeda_ Poverty and Equity Global Practice Group June 2017
Policy Research Working Paper 8104

# **Abstract**

Poverty estimates usually lag behind two years, which makes it difficult to provide real-time poverty analysis to assess the impact of economic crisis and shocks among the less well-off, and subsequently limits policy responses. This paper takes advantage of up-to-date average economic welfare indicators like the gross domestic product per capita and comprehensive harmonized micro data of more than 180 household surveys in 15 Latin American countries. The paper tests three commonly used poverty nowcasting methods and ranks their performance by comparing country-specific and regional poverty nowcasts with actual poverty estimates for 2003–14 period. The validation results show that the two bottom-up approaches, which simulate the performance of each agent in the economy to nowcast overall poverty, perform relatively better than the top-down approach, which uses welfare estimates to explain the performance of poverty at an aggregate level over time. The results are robust to additional sensitivity and robustness tests.

This paper is a product of the Poverty and Equity Global Practice Group. 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://econ.worldbank.org. The authors may be contacted at gcaruso@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
# **But... What Is The Poverty Rate Today? Testing Poverty Nowcasting Methods in Latin America and the Caribbean** 

German Caruso<sup></sup> Eduardo Malasquez<sup>†</sup> Leonardo Lucchetti<sup>§</sup> Thiago Scot<sup>‡</sup> R. Andrés Castañeda<sup>††</sup> JEL classification: D31, I3, I31, D6 _Key words:_ Poverty, Nowcasting, Latin America and the Caribbean, Validation We are grateful to Oscar Calvo-Gonzalez, Samuel Jaime Pienknagura, German Reyes, Liliana Sousa, Daniel Valderrama, Carlos Vegh, and Nobuo Yoshida whose suggestions greatly improved earlier drafts of the paper. All remaining errors are ours.

>  World Bank. E-mail: gcaruso@worldbank.org

§ World Bank. E-mail: llucchetti@worldbank.org † World Bank. E-mail: emalasquez@worldbank.org ‡ University of California at Berkeley. E-mail: thiago_scot@berkeley.edu †† World Bank. E-mail: acastanedaa@worldbank.org
# **1 Introduction**

Among all the socioeconomic indicators developed during the last two centuries, the share of the population living in poverty has become one of the most studied and monitored (Ravallion 2016, chap. 1). A good poverty measurement and profiling identifies the poor and targets and monitors all interventions designed to benefit the most disadvantaged groups in society. Thus, there is an increasing interest from academics and policy makers to know the current poverty status at the country, regional, and global levels to design policy solutions that alleviate the situation of the less well-off.<sup>1</sup> Nonetheless, due to data collection and processing time, poverty indicators are generally released with one or more years of lag. This delay makes it challenging to provide real-time poverty analysis and to strengthen the dialogue on the implementation of policies to mitigate the poverty impact of shocks like economic crisis or natural disasters.<sup>2</sup> Departing from the basic intuition that the performance of poverty depends on the evolution of national welfare aggregates like the GDP per capita, it is expected that poverty forecasting relies on the accuracy of forecasted GDP. That is, if the forecasted GDP were off, the forecasted poverty would be off as well. However, the main difference between nowcasting and forecasting poverty is that the GDP per capita is actual for the former, while it is forecasted for the latter. By validating three poverty forecasting methods with actual GDP information, this paper bridges the gap of knowledge between the most recent poverty numbers available and the current calendar year. Additionally, it provides empirical evidence for the reliability of such methods to enlighten the current situation of poverty, rather than its performance in the future.

Generally speaking, poverty forecasting provides a series of possible, future GDP scenarios whose poverty outcomes are determined by the poverty forecasting method. That is, poverty forecasting is an attempt to understand the performance of poverty if the GDP scenario assumptions are met and the poverty forecasting method is accurate (Karver, Kenny, and Sumner

> 1 For instance, extreme poverty reduction was among the most important indicators in the Millennium Development Goals (MDGs), while the World Bank recently adopted the goal of ending extreme poverty at the global level by 2030. The World Bank measures global overall poverty as life under a US$1.9 per person per day in 2011 Purchasing Power Parity (PPP) (Ferreira et al. 2016, Dean and Prydz 2015). Similarly, the World Bank estimates the regional overall poverty in the LAC region as having an income below the US$4 per person per day poverty line in 2005 PPPs (Gasparini et al. 2013, Castaneda et al. 2016).

> 2 For instance, the latest global poverty estimates produced by the World Bank are from 2013, while the most recent Latin American and the Caribbean regional estimates are from 2014 (see Castaneda et al. 2016 for the 2014 LAC regional estimates).

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2012; Ravallion 2012; Ravallion 2013; Edward and Sumner 2013; Chandy, Ledlie, and Penciakova 2013; Yoshida, Uematsu, and Sobrado 2014; and Poverty Research Report, The World Bank 2000). In contrast, given that poverty nowcasting relies on actual GDP data, its accuracy depends only on the features of each nowcasting method.

The purpose of this paper is to provide a comprehensive analysis of several methods for poverty nowcasting to get real-time poverty estimates in Latin America and the Caribbean (LAC). To this end, the paper first documents existing methodologies for poverty nowcasting by describing in detail their main assumptions, their information requirements, and their main limitations. Then, it validates the performance of these methods by comparing nowcasted poverty numbers with actual poverty estimates. In the particular case of the LAC region, National Statistical Offices (NSOs) usually release poverty numbers with one year of lag. Thus, this paper validates these poverty nowcasting methods one year ahead.

Three contributions to the literature on poverty nowcasting—and forecasting—stem from this paper. First, this paper develops a methodological framework to understand the errors of these techniques for poverty nowcasting. Second, this analysis validates the methods using a set of about 180 harmonized micro household datasets available for 15 countries in LAC for the 2003–14 period. By using this comprehensive database, the paper minimizes the possibility of arriving to conclusions based on biased samples of countries or spurious results. Finally, the paper assesses the robustness of the results and quantifies the accuracy of each method by empirically testing the magnitude of the errors in each methodology.

Our results suggest that the three methods are promising for nowcasting both large poverty reductions as well as poverty stagnation in the region one year ahead. In general, the two bottomup approaches that simulate the performance of each agent in the economy to nowcast poverty perform better than the top-down approach that uses welfare estimates to explain the performance of poverty at an aggregate level over time. The paper also provides evidence that the results are in general stable to changes in the underlying parameters used for producing poverty nowcasts.

The paper is organized as follows. Section 2 introduces the three approaches for nowcasting poverty and the theoretical framework of the nowcasting errors. Section 3 presents the data used and the empirical approach. Section 4 presents the validation results of the poverty nowcasting in LAC. Section 5 shows the stress and sensitivity analysis of the methods. Finally, section 6 concludes.

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# **2 Poverty forecasting methods in practice**

The projection of poverty headcount is nothing else than “ _non-linear functions of underlying changes in average income and measures of income inequality_ ” (Kraay 2006, 200). That is, the analysis of the performance of certain covariates that are assumed to have a significant and known effect on the welfare distribution, so that we are able to estimate the new share of population under a particular welfare threshold in a subsequent period for which there are no microdata available. The literature presents several methods to identify the main determinants and forecast poverty, though little is known about their level of accuracy and performance. These methods vary in terms of their assumptions and level of sophistication, which can be framed under two general approaches: “top-down” and “bottom-up” methods.

# _2.1 Top-down approaches_

These approaches use economic indicators like Gross Domestic Product (GDP) growth to explain the performance of poverty at an aggregate level over time. One of the top-down approaches most widely used is the Poverty-growth Elasticity (PE hereafter) method. The simplest version of this method consist of the ratio between the percent change in the poverty headcount and the percent change of a welfare aggregate measure –e.g., GDP per capita- in two moments in time, that is where ΔPt = Pt −Pt−1 is the change in the poverty headcount and ΔYt = Yt −Yt−1 is the change in the aggregate measure of welfare. Assuming that the elasticity Et,t−1 has a unique non-stochastic value over time for any poverty measure, poverty in period t+ 1 can be projected as follows Elasticities have proved to perform well for poverty forecasting in cross-country settings (Bourguignon 2003, Klasen and Misselhorn 2006, and Yoshida et al. 2014). However, it can be shown that the relationship between growth and poverty tends to decrease when poverty decreases and therefore they may not work properly when forecasting poverty rates in long periods of time (Yoshida et al. 2014).

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Kakwani (1993) proposes a methodology that assumes that the Lorenz curve shifts entirely by an offset factor,<sup>3</sup> which leads to a rigid structure of inequality but provides a useful simplification. With these in hand, the author calculates elasticities of poverty with respect to both changes in mean income and Gini coefficient. Results show that, for the case of Côte d’Ivoire, the measures of poverty are highly elastic to changes in income inequality and mean income, with the income elasticity being considerably higher. Dollar and Kraay (2002) and Kraay (2006) find different results for a large set of countries where the average income growth is the main and most important driver of poverty reduction. Similarly, Datt and Ravallion (1992) decomposes changes in poverty in Brazil and India in the 1980s, finding that the effect of growth on poverty overshadows the redistribution effect for most of the pairs of years studied. This implies that, depending on the country and its current characteristics, poverty might be determined either by the growth of the economy or by the distribution of welfare in a particular period.

By adding temporality to the analysis, Ravallion and Chen (1997, 360) suggest a simple model in which the Lorenz curve may change from one period to another. In this case, the elasticity can take any sign or magnitude and it has its own distribution, that is where B is an empirical growth elasticity, α is a time-persistent effect, and γ is a time trend. Given that it is impossible to observe the true mean of the GDP or consumption per capita Yt∗, the regressions must be done with what is actually observed, Yt.

More sophisticated models attempt to incorporate other aggregate variables like inequality, but given that several combinations of two or more aggregate variables may produce the same poverty forecast, the exercise must be done by assessing the plausibility of different scenarios (Ravallion 2012; Ravallion 2013).

# _2.2 Bottom-up approaches_

These approaches simulate the performance—or even the behavior—of each agent in the economy to generate a new welfare aggregate used to estimate poverty. The most basic model assumes that all households’ incomes are re-scaled by the same factor, say GDP per capita growth (Yoshida et al. 2014). This method, known as Neutral Distribution Growth (NDG hereafter), usually performs

> 3 Namely, L∗(p) = L(p) −λ[p−L(p)], where L is the original Lorenz curve, L∗ is the shifted one, and λ is the percentage change of the Gini coefficient.

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well as long as inequality remains stable. Karver, Kenny, and Sumner (2012) explain that poverty forecast based on past trends is a naïve approach to forecasting due to the high volatility of poverty. Instead, they select three different scenarios based on IMF growth projections and predict poverty rates for all countries, assuming static inequality in a 20-year period. As explained by the authors, the assumption of a neutral distribution is strong and it may bias the results in exercises that involve long-run predictions like theirs. In this paper, in contrast, the validation of poverty estimates is done from one year to another; a small period of time in which inequality changes are null or very small, especially in LAC where income inequality has decreased considerably in the past decade in most of the countries and then recently stagnated (Cord et al. 2017).

Complex models in which income distribution is not assumed stable provide deeper understanding of the relation between specific segments of the economy and the evolution of poverty rates. Olivieri et al. (2014) developed a technique and software module—ADePT Simulation—to forecast the distribution of incomes by incorporating projections of other aggregates such as economic output and employment by sector; prices; and population growth. Other methods disaggregate the country’s population into proportionally-augmented bands of welfare aggregates in order to relax the assumption of static distribution (Edward 2006; Edward and Sumner 2013), or simply assume different inequality scenarios by shifting the proportion of economic growth from the top 10 percent to the bottom 40 (Chandy, Ledlie, and Penciakova 2013). The main advantage of the method is that it produces income forecasts at the household-level and allows predicting distributional measures besides poverty. However, data requirements are significant and therefore it is costly to apply the method to several countries at the same time and in a consistent manner, which is one of the main objectives of this paper.

# _2.3 The approach of this paper_

The two approaches most widely used today to nowcast poverty are the PE and the NDG methods. Although simple to implement, the PE method has limited application because it produces only aggregated -as opposed to household or individual level- poverty extrapolations. On the other hand, unlike the PE method, the main advantage of the NDG method is that it produces income estimates at the household-level. However, since all household incomes are multiplied by the same economic growth rate, the method cannot be used for distributional analysis.

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To overcome these limitations, we also analyze a generalized form of the NDG method, in which different sections of the income distribution are assumed to grow at different rates, following a specific and ad-hoc algorithm. This approach attempts to capture the heterogeneity of growth across individuals or households by assuming that quantile-specific contributions to growth during a known-data period remain similar during the unknown-data period. This assumption is an extension of the “share of incremental income” definition of pro-poor growth studied by White and Anderson (2001). The authors explain that if the share of total income growth (Yt −Yt−1) that corresponds to the income growth of the poor (YtP −Yt−1P ) from time t−1 to t is higher than from t−2 to t−1, the economy can be classified as pro-poor. Instead of studying the contribution of the poor population, which varies over time, we analyze the contribution of each quantile to total growth and assume stability over time. We refer to this method as Quantile Growth Contribution (QGC).

Two main assumptions are required under QGC. First, the method assumes that people with similar welfare aggregates in one period will perform similarly in the next period. That is, we expect that, after ranking the population by quantiles based on welfare, two households within the same quantile in period _t_ will belong to the same quantile in period t+ 1. Second, the method assumes that the economy performs today as it did in the past.

Data requirements needed to implement all these three methods are fairly reasonable and therefore they can be applied in our setting: to nowcast poverty estimates in many countries and years and in a consistent manner. In addition, all these methods have real-life applications and have been extensively used to nowcast and forecast poverty estimates. For instance, the World Bank uses the NDG method to extrapolate poverty estimates from the latest surveys available (Yoshida et al. 2014), while it uses the PE method to produce poverty forecasts based on per capita GDP forecasts (World Bank 2015; Yoshida et al. 2014).

# **3 Analytical assessment of measuring poverty in real time**

# _3.1 Poverty measurement in the world and in LAC_

Since the early 1990s, the World Bank has measured global poverty based on a comparable total household per capita welfare measure and an international poverty line, both expressed in the same purchasing power in all countries of the world (Ferreira et al. 2016). In the particular case of LAC, income is the proxy for welfare most commonly used. Even when consumption is usually preferred 7
in the literature, income has been widely used in practice in the region since consumption is rarely collected by the national statistical offices (NSOs) in LAC.

Due to the time required for household data collection and processing, household surveys are usually available only with a two or more years lag. This makes it extremely challenging to provide real-time poverty analysis. Although LAC is the region with most frequent household surveys, the region is not an exception; the latest data available are from 2014 in most of the countries in the region. To address this knowledge gap, this paper provides validations of three alternative methods widely applied to nowcast poverty estimates both at the country as well as at the regional level and provides up-to-date poverty estimates in the region.

Despite being outdated, poverty data in LAC are more up-to-date than most of other regions in the world. In addition, the quality of the data is usually superior in many dimension. For instance, surveys have in general more coverage –i.e., over 90 percent of LAC’s population is covered by poverty data since the 1990s -- data are more frequent –i.e., about 60 percent of the countries in LAC have more than three data points (Serajuddin et al. 2015)-, and surveys are available for many years and usually comparable over time in most of the LAC countries. Having several years of data offers at least two advantages. First, the years considered (2003-14) coincide with a period of large poverty drops as well as poverty stagnation, which allows us to validate methods under different scenarios of poverty changes. Second, having several years allows us to test the robustness of some methods to the use of different past information. For all these reasons, this paper focuses in the LAC region to validate existing poverty nowcasting methods.

# _3.2 Methods used for poverty nowcasting_

This section presents the data environment and the three methods used to nowcast poverty estimates. The analysis is performed in three periods of time: periods –2, –1, and 0; the first two periods refer to the past when household surveys and national accounts information are available, while period 0 refers to the present when _only_ national accounts information is available. Notice that the sequence in the nomenclature of the periods (i.e., –2, –1, and 0) does not imply that they are adjacent or subsequent to each other; rather that the sequence is in a chronological order where each period could be several years apart from the other. For the sake of simplicity we neglected population growth in our estimations, as nowcasting generally implies very short periods of time in which data availability is missing and for which population growth is usually negligible.

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# _3.2.1 The Poverty-growth Elasticity method_

The PE method computes the GDP per capita growth elasticity of poverty between –2 and –1 and uses that information to nowcast poverty in moment 0. The World Bank currently uses this method to produce poverty forecasts based on GDP per capita forecasts.<sup>4</sup> Let yit be the total household per capita income for household _i_ in moment _t_ , P(yt) is the corresponding poverty rate in moment _t_ defined as the proportion of the population with household t,t−1 income lower than a poverty line _z_ ;<sup>5</sup> g<sup>t</sup> the GDP per capita in moment _t_ ; rg the real GDP per capita growth rate between t and t−1; and ε<sup>t,t−1</sup> the GDP per capita growth elasticity of poverty between t and t−1. Poverty in moment 0 is defined as: However, notice that the value of ε<sup>0,−1</sup> is unknown, since it depends on the actual value of poverty in period 0. However, if ε<sup>0,−1</sup> is assumed to be a unique nonstochastic value over time for any poverty measure, the elasticity between –1 and –2 is an approximation for the unknown elasticity between 0 and –1.<sup>6</sup> Then, poverty nowcast in moment 0 is obtained as follows: where P(y<sup>0</sup> )<sup>E</sup> refers to nowcasted poverty in period 0 obtained from applying the PE method.

The PE method does not use household-level microdata; it only uses aggregated GDP per capita and poverty indicators -i.e., there is no subscript _i_ in equation (5). The level of accuracy of the PE method depends on how similar ε<sup>−1,−2</sup> and ε<sup>0,−1</sup> are -i.e., how accurate is the past information used to estimate the unknown elasticity.

# _3.2.2 The Neutral Distribution Growth method_

The NDG method assumes that all households’ incomes are affected by the same factor—generally GDP per capita growth—from period –1 to period 0. However, given that GDP per capita growth encompasses more economic elements than household income, its growth rate is usually different from the household income growth rate. Let θ be the adjustment factor that accounts for the

> 4 See World Bank (2015).

> 5 Given that we are using a constant, real value for the poverty line, we ignore _z_ in this analysis. 6 Section 5 tests the sensitivity of the method to the selection of other periods.

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difference between GDP per capita and per capita household income growth -known as passthrough. The NDG method produces poverty nowcasts in moment 0 as follows: where ỹig0 is household _i_ ’s nowcasted income obtained from applying the NDG method, and P(ỹg0) the corresponding poverty rate. Unlike the PE method, the NDG method uses household-level microdata to nowcast poverty –i.e., subscript _i_ is considered in the equation (6)and it does not use information between periods -1 and -2.

The NDG method assumes that the total household per capita income growth rate is the same across households<sup>7</sup> and that the pass-through θ is known.<sup>8</sup> <mark>The more similar income growth across households is and the more knowledge we have about the pass-through, the more accurate the poverty nowcasting produced under the NDG method is. Nowcasting</mark> errors will occur whenever per capita income growth differs across households and whenever we use a pass-through value which differs from the actual one.

# _3.2.3 The Quantile Growth Contribution method_

Unlike the NDG, the QGC method does not assume that the household per capita income growth rate is the same across households. The QGC method captures the heterogeneity among households by assigning different growth rates along the income distribution. Since we do not have panel data for most countries, it is not feasible to determine the individual performance of each household between two periods. Assuming that people with comparable welfare levels in one period will perform similarly in the following one, the QGC method assigns individual growth rates in a twostage process.

In the first stage of the process we group households into income-sorted quantiles and calculate the contribution of each quantile to total growth between -2 and -1. Generally, the total growth of the economy between _t-1_ and _t_ may be seen as the sum of the growth of all quantiles q,

> 7 The method assumes that (yity−yit−1it−1) = (yjty−yjt−1jt−1) = θ∗rgt,t−1 for all households i≠j.

> 8 In this paper we use θ= 1 as the default option. Section 5 tests the sensitivity of the method to the value of the passthrough.

10
where Y<sup>t</sup> = ∑(yi it) is the total income of the economy, Yqt is the total income of quantile _q_ in t,t−1 9 period _t_ , and rq is the growth rate of total income of quantile q from period _t_ to period _t–1_ .

We then assume that the contribution of each quantile to total growth in the unknown-data period (i.e., -1 and 0) is the same as the contribution in the known-data period (i.e., -2 and -1), that is ΔY−1,−2 where Ŷq0 is the nowcasted total income of quantile _q_ in moment 0 and Sq−1,−2 = ΔYq<sup>−1,−2</sup> is the contribution of quantile _q_ to the total income growth between -1 and -2.

The second stage of the process is to distribute Ŷq0 among households i in quantile q. We consider two different approaches. The first approach assumes a democratic scenario in which all households within a quantile receive the same per-capita income amount.

−1 where nq is the number of households in quantile q in moment –1. This approach underlines the assumption that households within the same quantile are similar. The second approach, a plutocratic scenario, assumes that each household receives an amount of income based on its share of the total income within its quantile in period -1.

Whereas the plutocratic approach considers relative differences between households within the same quantile, the democratic approach is less intuitive but straightforward. In this paper, we use the former. Replacing (8) in (10) and assuming no population growth, the characterization of household _i_ ’s income under the QGC method is

> 9 −1,−2 Notice that if growth rates rq were the same rate _r_ for all quantiles, we would be under the NDG scenario (ΔY<sup>−1,−2</sup> = r<sup>−1,−2</sup> ∗Y<sup>−2</sup> = θ∗rg−1,−2Y−2).

11
This paper does not attempt to prove the goodness of fit of any of these methods. Each method has its own assumptions and properties, which are validated under actual data scrutiny. Notice that the QGC approach, in particular, is not an improvement of the NDG approach, but the same methodology under different assumptions. The NDG assumes that all households—and therefore quantiles—grow at the same pace, whereas QGC assumes that each quantile grows according to its contribution to total growth in a known-data period.

# _3.3 Theoretical framework for nowcasting errors_

As discussed in section 3.2, all methods need to make some assumptions in order to produce poverty nowcasts in period 0 –i.e., knowledge of the elasticity, the pass-through, and the contribution of every household to the change in total incomes. Therefore, errors will arise whenever those assumptions are not met. This section presents the errors that arise from all these assumptions.

# _3.3.1 Error under the PE method_

The main assumption of the PE method is that the value of the elasticity between 0 and -1 is known. However, that elasticity is unknown and needs to be estimated in reality. In this paper we use the value of the elasticity between -1 and -2 as an approximation. Of course an error will occur whenever this approximation is not accurate. The error can be expressed as: According to equation (12), the size of the error depends on the past information used for nowcasting -i.e., on how similar ε<sup>−1,−2</sup> and ε<sup>0,−1</sup> are. The error will be zero whenever ε<sup>−1,−2</sup> and ε<sup>0,−1</sup> are equal. We will refer to this error as the _Informational Error_ (IE).

# _3.3.2 Errors under the NDG method_

The NDG method makes two assumptions: (i) equal per capita income growth across all households and (ii) full knowledge of the pass-through θ. Errors will occur whenever any of these 0,−1 two assumptions are not met. Let ry be the “unobserved” growth of per capita incomes between 0 and -1, ỹi0 be household _i_ ’s income in moment 0 that arises from multiplying household _i_ ’s 12
income in moment -1 by this income growth between 0 and –1, and P(ỹg0) the corresponding poverty rate:<sup>10</sup> The error can be expressed as: Following the notation used by Datt and Ravallion (1992), since poverty changes only due to changes in mean income relative to the poverty line or in the relative income inequality, then poverty measures in moment _t_ can be characterized by a poverty line _z_ , the Lorenz curve L<sup>t</sup> , and the mean of the welfare distribution μ<sup>t</sup> . In addition, given that both ỹi0 and ỹig0 come from rescaling household _i_ ’s income in moment -1, yi−1, then these three incomes have the same relative distribution represented by the Lorenz curve L<sup>−1</sup> . Then, the error of the NDG method is the following: The term [P(μ<sup>0</sup> , L<sup>0</sup> ) −P(μ<sup>0</sup> , L<sup>−1</sup> )] is the error that results from distributing household income growth evenly across all households in period -1. We will refer to this as the _Distributional Error_ (DE). The more similar is the income growth among all households, the closer to zero DE is. On the other hand, the term [P(μ<sup>0</sup> , L<sup>−1</sup> ) −P(μg0, L−1)] is the error that results from re-scaling 0,−1 0,−1 all incomes by the GDP per capita growth rg instead of the income growth ry . We call this the _Pass-through Error_ (PTE). The closer to one is the actual pass-through, the closer to zero the PE is. Since the NDG method does not use past information, there is no IE. Similarly, there is no DE and PTE under the PE because the PE does not use household-level micro data.

# _3.3.3 Errors under the QGC method_

There are three characterizations of the QGC. First, unlike the NDG, the method does not assume that income growth is the same among all households. Second, like the NDG method, the QGC

> 10 Since ry0,−1 is unobserved, ỹi0 cannot be obtained with actual data. However, these values allow us to characterize the errors that arise from re-scaling all individual incomes by the GDP growth instead of actual household income growth.

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assumes that the pass-through θ is known. Finally, like in the PE method—and unlike the NDG method—, the QGC also uses past information (that does not necessarily reflects the present situation). Therefore, all three errors are present under the QGC method: the IE, PTE, and DE.

Let Sq0,−1 be the “unobserved” contribution of quantile _q_ to total income growth between 0 and -1 and let ŷiqy0 be household _i_ ’s income in moment 0 that arises from multiplying income in moment -1 by the “unobserved” per capita income growth between 0 and -1 and by distributing −1 0,−1 yiq 0 that growth according to Sq ∗ Y (and P(ŷy ) the corresponding poverty rate): q<sup>−1</sup> In addition, let ŷiqg0′ be household _i_ ’s income in moment 0 that arises from multiplying income in moment -1 by the GDP per capita growth between 0 and -1 and by distributing that −1 0,−1 yiq 0<sup>′</sup> 11 growth according to the “unobserved” Sq ∗ Y (and P(ŷg ) the corresponding poverty rate): q<sup>−1</sup> Then, the error of the QGC is: where L<sup>t′</sup> is the Lorenz curve that arises from allocating income or GDP per capita growth according to Sqt−1,t. The term [P(μ0, L0) −P(μ0, L−1′)] is the error that arises from allocating household per capita income growth to all households in period -1 according to Sq0,−1. This is the equivalent to _Distributional Error_ (DE). The more similar is the income change among households within quantiles, the closer to zero will be the DE. The term [P(μ<sup>0</sup> , L<sup>−1′</sup> ) −P(μg0, L−1′)] is the

> 11 Since Sq0,−1 and ry0,−1 are unobserved, ŷiqy0 and ŷiqg0′ cannot be obtained with actual data. However, these values allow us to characterize the errors that arise from nowcasting using the QGC method.

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0,−1 error that results from re-scaling all incomes by the GDP per capita growth rg instead of the 0,−1 income growth ry . This is the equivalent to the _Pass-through Error_ (PTE); this error will get closer to zero whenever we use a pass-through similar to the actual one. Finally, [P(μg0, L−1′) − P(μg0, L−2′)] is the error that arises from using information from the past that does not reflect the present information. This error is equivalent to the _Informational error_ (IE) in the PE method.

# **4 Data and empirical approach for validating poverty nowcasts**

_4.1 Per capita household income from harmonized household surveys in LAC_ In order to measure country-specific and regional poverty in this paper, we need to increase cross country comparability of welfare measures and poverty lines. Since the LAC region is the focus of the paper, we use the $4 per person per day moderate poverty line in 2005 PPP to measure poverty. In addition, we use the SEDLAC micro data as the primary source of the comparable welfare aggregate. The SEDLAC project is a harmonized micro database of LAC’s main households’ surveys produced by the poverty group at the World Bank in partnership with the Center for Distributive, Labor, and Social Studies (CEDLAS, for its acronym in Spanish) at the Universidad Nacional de La Plata in Argentina.<sup>12</sup> The main goal of this project is to increase crosscountry comparability of many socioeconomic indicators, including total household per capita income, from more than 300 household surveys within 18 countries spanning more than 20 years of surveys.<sup>13</sup> The SEDLAC project has been increasingly used by researchers in the analysis of poverty and inequality in LAC. However, unlike many other past studies, this paper uses the micro data instead of country-level indicators produced by SEDLAC. All nowcasting methods are validated for all countries in LAC for which data are frequently collected during the 2003-14 period.<sup>14</sup> Table 1 introduces all surveys (and their coverage) used in this paper.

> 12 See Castaneda et al. (2016), Bourguignon (2015), and Gasparini, Cicowiez, and Escudero (2013) for a more detailed description of the SEDLAC project.

> 13 Since the main goal of the SEDLAC project is to enhance cross-country comparability, poverty measures in this paper are not comparable to those published by NSOs in the region (Castaneda et al. 2016). 14 Guatemala and Nicaragua have fewer than four years of data and therefore they are excluded from the validation (section 3) and sensitivity (section 4) analysis.

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_4.2 Empirical approach for testing and improving poverty nowcasting methods in LAC_ We select a default value for all parameters used in the estimations. First, we assume a passthrough θ= 1 for the NDG and QGC methods. Second, all past information is obtained from periods -1 and -2 when nowcasting poverty in moment 0 –i.e., we compute ε<sup>−1,−2</sup> and Sq−1,−2 in the PE and QGC methods respectively. Third, we set the number of quantiles q = 20 under the QGC method.

In order to assess the validity of the three nowcasting techniques we compare the nowcasted poverty rates in period 2005-14 with the actual poverty rates in all countries for which poverty data are available more than three times in the period 2003-14. For instance, let’s assume that we are interested in nowcasting poverty in 2005. Poverty nowcasted under the PE method is: Similarly, nowcasted incomes under the NDG method are: Finally, incomes nowcasted under the QGC method are: These results are compared with the actual poverty rate in 2005 in order to assess the validity of the three methods. The same procedure is then repeated for all years in the 2006-14 period.<sup>15</sup> Finally, we change the value of the default parameters –pass-through, periods used to compute past information, and number of quantiles- in order to test the sensitivity of the estimates.

# **5 Validation of poverty nowcasting methods in LAC**

# _5.1 Country-specific validations_

We start by comparing actual poverty estimates with the nowcasted poverty that is obtained from applying all three methods described in previous sections. Figure 1 presents these comparisons for all countries in LAC for which data are available between 2003 and 2014 on a regular basis (shown in detail in appendix table A.1). In general, all methods perform reasonably well and all countryspecific poverty nowcasts are close to the actual poverty rates –i.e., all estimates are neighboring the 45 degree line. The NDG method performs better in most of the cases. We note that the QGC

> 15 We compare with an interpolated mid-point value whenever there is no actual poverty rate available.

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and, in particular, the PE tend to be more dispersed around the 45 degree line and they have several outliers in a number of cases.

Table 2 and Figure 2 confirm these results. Table 2 shows a set of statistics of the aggregated errors under the three methods, while Figure 2 presents the histogram of those errors. Country-specific aggregate errors defined as the difference between poverty nowcasts and actual poverty rates are quite small in general and the NDG tends to slightly outperform the other two methods. On average, country-specific poverty nowcasts tend to be three percent higher than the actual poverty rates under the NDG, while they tend to overstate actual poverty by about 5 percent under the other two methods. As expected, the correlation between actual and nowcasted poverty is higher under the NDG (0.98) than the QGC and PE methods (0.85 and 0.73, respectively).

However, the QGC method outperforms the NDG once the outliers are taken into consideration. The median of the nowcasting errors –a measure more robust to extreme values and outliers- is about three times higher under the NDG when compared with the other two methods. Therefore, good use of past information is key to produce nowcasts of good quality –i.e., to minimize the IE- under the PE and QGC methods.<sup>16</sup> Table 2 and Figure 2 also confirm a higher dispersion of poverty nowcasting errors under the PE and QGC methods; the standard deviation of country level errors is about four times higher than those of the NDG method. However, even when having large dispersion, errors under the QGC tend to be more concentrated around zero than the PE. More than 87 percent of the cases analyzed have nowcasting errors lower than 20 percent in absolute terms under the QGC and the NDG methods, while less than 79 percent of the cases under the PE method.

# _5.2 Regional and sub-regional level validations_

At the regional and sub-regional levels, the performance of the methods differs from the country level one. Table 3 shows actual and nowcasted regional and sub-regional poverty estimates under the three methods for the period 2005-14, while Figure 3 shows the poverty nowcasting errors in percentages. The three methods perform well in general terms. With the exception of Central

> 16 Since errors and outliers cannot be inferred in advance, outliers cannot be removed ex-ante. However, presenting the median highlights the fact that NDG outperforms QGC in absence of the outliers produced by the latter method. In addition, the table also shows that Elasticity is outperformed by the other two methods even after considering outliers. Moreover, Table 2 helps understanding the risks associated with both QGC and PE methods in terms of the outliers that may result from using past information.

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America, correlation between nowcasting and actual poverty estimates are above 70 percent under the three methods, and over 0.90 for the NDG and the QGC.

PE tends to be outpaced by the other two methods. Aggregate errors, defined as the difference between poverty nowcasts and actual poverty rates, are quite small in general. In fact, the QGC performs slightly better than the NDG method when computing regional poverty nowcasts. For instance, the LAC average errors are about 1, 3, and 4 percent under the QGC, NDG, and PE methods, respectively. Once again, the PE and the QGC are relatively more dispersed than the GND.

Results under the QGC and NDG methods are encouraging both at the country and the regional levels. Validations show a good performance of both methods. The next section presents a series of sensitivity tests to changes in the default underlying parameters.

# **6 Stress and sensitivity analysis of poverty nowcasting methods in LAC**

In this section we test the robustness of the findings to changes in the underlying parameters –i.e., past information, pass-through, and number of quantiles used when nowcasting regional and country-level poverty rates. We perform all these test on the 15 countries for which data are available on a regular basis and for LAC as a whole.

# _6.1 Sensitivity analysis of the Informational Error_

The PE and QGC validation results use information on poverty elasticity and contribution to growth from periods -2 and -1 when nowcasting poverty in moment 0. However, with few exceptions, the 15 countries used in the analysis have micro data available on a yearly basis since 2003. This allows us to test whether the time span matters. For instance, we are interested in testing whether results are improved when using poverty elasticity and quantile contribution to growth between 2011-13 instead of 2012-13 when nowcasting poverty in 2014. The objective is to study the sensitivity of the PE to changes in the length of the period used to estimate the poverty elasticity and the quantile contribution to growth.

Table 4 shows 2014 poverty nowcasts for a range of periods for QGC and PE and keeping everything else unchanged. The table shows that the methods perform similarly irrespective of the length of periods used to estimate elasticity and growth contribution. However, there are a few exceptions for both QGC and PE, which can lead to outliers like the ones observed in Figure 1. For instance, QGC nowcasts increase significantly from 7.6 percent to 55 percent in Chile when 18
using the 2013-11 period instead of the 2013-12 one. Therefore, as mentioned in the previous section, these exceptions reinforce the idea that past information is key to produce nowcasts of good quality under the PE and QGC methods.

# _6.2 Sensitivity analysis of the Pass-through Error_

All previous poverty nowcasts under the QGC and NDG were computed using a pass-through θ= 1. However, any value selected would be arbitrary since income growth from surveys tends to differ from GDP per capita growth. Table 5 analyzes the sensitivity of 2014 nowcasts to the value of the pass-through. The objective is to study the sensitivity of the PTE to changes in the passthrough value keeping everything else unchanged. In general, the two methods perform similarly irrespective of the value of the pass-through selected and results are robust to the underlying assumption of the value of the pass-through.

# _6.3 Sensitivity analysis of Distributional Error_

Poverty nowcasts in section 4 were done using 20 quantiles under the QGC method. A relevant question is whether the QGC performs well at nowcasting regional and sub-regional poverty estimates when changing the number of quantiles. Table 6 shows 2014 poverty nowcasts using a large set of quantiles from 5 to 100 and keeping everything else unchanged. The objective is to study the sensitivity of the DE to changes in the number of quantiles. In general, the QGC method performs similarly irrespective of the number of quantiles selected.

# **7 Conclusions**

LAC has witnessed an impressive poverty reduction since 2003. Unfortunately, given that data are usually available with more than one year lag in the region, we cannot say much yet about the poverty impact of the lower economic growth that the region is currently experiencing. There are several methods to forecast and nowcast poverty estimates, however little is known about their level of accuracy and performance. To overcome this limitation, we use a comprehensive set of about 180 harmonized micro household surveys available in 15 LAC countries from 2003 to 2014 to analyze the performance of three different forecasting methods: (i) the Poverty Elasticity (PE), (ii) the Neutral Distribution Growth (NDG), and (iii) the Quantile Growth Contribution (QGC) methods.

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Results show that the three methods perform well at nowcasting large poverty reductions as well as poverty stagnation in the region in the 2005-14 period. After comparing nowcasted with actual poverty rates, in general we find the NDG and the QGC to be the best performers. However, the PE and the QGC outperform the NDG once extreme values are taken into consideration, meaning that good use of past information on poverty elasticities and quantile contributions to growth is key for producing good quality poverty nowcasts under the PE and QGC methods. The results are robust to a broad range of stress and sensitivity tests to changes in the underlying parameters.

The use of validated methods for poverty nowcasting by researches and international organizations is scarce, which is surprising in light of the massive acceptance that some of these techniques have in closely related areas (for instance, for nowcasting GDP estimates). For this reason, we stayed as close as possible to the standard nowcasting literature, relegating more sophisticated approaches, such as the use of satellite data to produce real-time poverty information, for further research. Our validation results provide support to the implementation of these methods for poverty nowcasting, which is for guiding the regional debate on poverty measurement in LAC.

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