What is Behind the Decline in Poverty Since 2000? Evidence from Bangladesh, Peru and Thailand

This paper quantifies the contributions of different factors to poverty reduction observed in Bangladesh, Peru and Thailand over the last decade. In contrast to methods that focus on aggregate summary statistics, the method adopted here generates entire counterfactual distributions to account for the contributions of demographics and income from labor and non-labor sources in explaining poverty reduction. The authors find that the most important contributor was the growth in labor income, mostly in the form of farm income in Bangladesh and Thailand and non-farm income in the case of Peru. This growth in labor incomes was driven by higher returns to individual and household endowments, pointing to increases in productivity and real wages as the driving force behind poverty declines. Lower dependency ratios also helped to reduce poverty, particularly in Bangladesh. Non-labor income contributed as well, albeit to a smaller extent, in the form of international remittances in the case of Bangladesh and through public and private transfers in Peru and Thailand. Transfers are more important in explaining the reduction in extreme compared with moderate poverty.


Introduction
Despite the global financial crisis, the incidence and depth of poverty has fallen in the majority of countries over the past decade, whether one uses national or international poverty lines. 1 What are the factors behind the observed poverty and distributional changes? Was the reduction in poverty a result of higher employment, higher productivity or higher transfers from public or private sources? Was it the result of changes in the sector composition of employment? Were these changes the result of improved human capital characteristics or higher returns to those characteristics?
Answers to these questions can contribute to the evidence base for policy going forward. For example, in some countries in Latin America there is a debate around whether the reduction in poverty and inequality over the last decade can be attributed to better job opportunities or to the expansion of more effective transfer policies. Was Brazil's success in reducing poverty and inequality despite modest growth due to the availability of better jobs or thanks to social policies? In South Asia, some question whether the reduction in poverty was on account of better job opportunities at home, or due to higher remittances. In East Asia several countries have seen strong growth and poverty reduction, but are lately questioning whether social policy should have a stronger focus on redistribution.
In this paper we use decomposition methods to quantify the contribution of different factors towards poverty reduction in three emerging economies over the last decade. Standard decomposition methods include the Datt- Ravallion (1992) method, which split changes in poverty into distribution-neutral growth, a redistributive effect and a residual. Kolenikov and Shorrocks (2005) decompose changes in poverty into growth, distribution and price effects, while Ravallion and Huppi (1991) offer a way of decomposing changes in poverty over time into intrasectoral effects, a component due to population shifts and an interaction term between sectoral changes and population shifts. However, the usefulness of these decomposition methods is limited by the fact that they explain changes in poverty on the basis of changes in summary statistics (Ravallion 2001). In contrast, the methods adopted in this paper generate entire counterfactual distributions, allowing us to decompose the contributions of changes in different sources of income and in individual and household characteristics to the observed distributional changes. As such, these methods can capture the heterogeneity of impacts throughout the distribution and allow us to distinguish the forces behind the observed outcomes. 2 4 specific patterns across the income distribution vary across countries, and the potential role of the different factors in reducing poverty is clearly different. Moreover the starting points are very different. Despite strong growth, Bangladesh is still a low-income country, with a GDP per capita of US$1,710, while Peru and Thailand are firmly in the middle-income country ranks with GDP per capita of US$10,439 and US$9,630, respectively (all figures in PPP terms). Peru is already highly urbanized, as opposed to Thailand and Bangladesh where the share of urban population is still below 30 percent.
The main result that emerges is that the largest contributions to poverty reduction in all three countries were labor market-related factors. The contributions to moderate poverty reduction on account of labor markets amount to 61 percent in Bangladesh, 75 percent in Peru and 65 percent in Thailand. Within this, the increase in the returns to endowments or characteristics explains most of the observed poverty reduction, pointing to an increase in real wages and higher productivity as the main contributors to poverty reduction in each case. While increases in farm income were mostly responsible for poverty reduction in Bangladesh and Thailand, non-farm income was mostly responsible in the case of Peru. Finally, while non-labor income played an important role in Thailand and Peru, particularly in reducing extreme poverty, the results show that labor income-from farm or non-farm sources-was the main contributor to poverty reduction.
The rest of the paper is organized as follows. Section 2 describes the evolution of poverty and economic growth in Bangladesh, Peru and Thailand, highlighting the similarities and differences in the initial and end period outcomes. Section 3 presents a simple approach, the results of which serve as a basis for the in-depth approach presented in Section 4. Section 5 concludes.

Country Context
Bangladesh, Peru and Thailand have one thing in common: they were able to drastically reduce poverty rates during the past decade. Using national moderate poverty lines, poverty fell by 1.8 percentage points per year in Bangladesh between 2000 and 2010, 2.7 percentage points per year in Peru between 2004 and 2010 and 1.6 percentage points per year in Thailand between 2000 and 2009. 6 Using an international poverty line of US$2.50 a day, these figures are -0.5, -1.4 and -0.6 percentage points annually for Bangladesh, Peru and Thailand respectively ( Figure 1A). 7 Moreover, these countries all experienced strong growth over the decade, averaging 5.8 percent annually in Bangladesh, 6 percent in Peru and 4.4 percent in Thailand ( Figure 1B). Greater volatility and vulnerability to the financial crisis was observed in Thailand and Peru, while Bangladesh enjoyed uninterrupted growth throughout the decade. 5 There is considerable evidence that economic growth is strongly and negatively correlated with changes in poverty (Ravallion and Chen, 2007). Using the standard Datt-Ravallion decomposition, growth does indeed explain most of the observed reduction in poverty in all three countries (Table 1). In each case, more than 90 percent of the observed change in poverty is explained by growth in mean income, while better distribution explains less than 10 percent of these changes.
Labor income, which has grown across the income distribution in all cases, could explain the transmission mechanism behind growth and the observed changes in poverty reduction (Figure 4). Those at the top of the income distribution in Bangladesh have seen their labor incomes grow faster than those at the bottom, while in Peru the opposite is true. In Thailand, incomes of the poor grow faster, except for those on the poorest decile. Given the magnitude of the changes, it is likely that growth in labor incomes did have an influence in moving people out of poverty.
Moreover, summary statistics show that labor force participation has remained relatively stable in Bangladesh and Thailand, while the employment population ratio increased slightly. On the other hand, in Peru both labor force participation and employment have increased, particularly for women ( Figure 5 and Table 2). At the household level, we find that the share of occupied adults has increased in both Bangladesh and Peru (Table 2). However, in the case of Thailand, we find a slight decline in the share of occupied adults, possibly pointing to the impact of an aging population that could negatively affect consumption per capita.
But other structural factors might explain changes in poverty. First, demographics could play a role. Population growth has slowed considerably in each of the countries considered, and has been significant enough so that in the case of Bangladesh and Peru the youth bulge observed in earlier periods has now reached a working age, 8 meaning these are countries starting to enjoy a -demographic bonus‖ ( Figure 2). This is also evident by the observed decrease in the average household size and a slight increase in the number of adults in each household ( Figure 3 and Table 2). In principle, higher numbers of adults per household imply lower dependency rates, and therefore potentially higher consumption per capita. The question is how important this effect was in the observed changes in poverty during the past decade.
Another factor that could be behind the observed reductions in poverty is growth in non-labor income. Public and private transfers have been steadily increasing in Bangladesh, Peru and Thailand over the last decade ( Figure 6). With regard to private transfers, international remittances have tripled in Bangladesh over the last decade, and have modestly grown in Peru. In Bangladesh, they amount to 5 percent of GDP, in Peru 2 percent and in Thailand 0.6 percent. They could be an important cushion to income shocks, but can also be greatly affected by conditions in the host country. 6 While there are important differences in terms of the magnitude of public social spending across countries relative to the size of their economies, public spending has increased by at least 25 percent over the decade in each country. The importance of public transfers in explaining poverty reduction depends on its importance as a share of total consumption of the poor and the effectiveness of this spending, particularly in terms of targeting and in generating the right behavioral incentives among the poor. 9 Cash transfers, for example, may directly decrease monetary poverty through increasing disposable income. But they can also have an additional impact as they may allow credit constrained families to invest in productive assets.
Finally, in the context of growing incomes, households are likely to change the share of income they dedicate to consumption. The consumption-to-income ratio has fallen over the course of the decade in Bangladesh and Thailand, but it has increased in Peru (Figure 7). As a result, when undertaking the decompositions, this change will contribute to poverty reduction in the case of Peru (as a greater share of income is consumed), while it will imply a negative contribution to poverty reduction in the case of Bangladesh and Thailand, where the observed changes in consumption will seem less dramatic than what we would have otherwise expected had the consumption-to-income ratio remained constant. Since poverty is measured by consumption, actual poverty rates in Bangladesh and Thailand will be higher in the final period than they would have been had the consumption-to-income ratio remained constant.

A Simple Approach
While the standard Datt- Ravallion (1992) estimates of the reduced-form relationships between economic growth, inequality and poverty have been useful to identify empirical regularities, they are unable to make explicit links in how growth and poverty reduction are related (Ferreira, 2010). To go a bit beyond this, we begin with a simple approach, which requires only an accounting identity on household consumption and income, rather than a full behavioral model, but still allows us to distinguish the contributions to poverty reduction on account of changes in demographics, public and private transfers, labor income and changes in consumption patterns. Household consumption per capita is defined by: (1) where is household income, n is the number of household members and is the consumption-to-income ratio, which includes both the marginal propensity to consume and any measurement error. 7 Since the distribution of welfare depends on the distribution of consumption per capita, four forces could have a potential impact on poverty reduction: (1) a reduction in the number of household members, which, holding all else equal, could imply higher levels of consumption per member; (2) growth in labor income, which could lead to higher consumption; (3) growth in non-labor income; and (4) changes in the consumption-to-income ratio. We consider each of these in turn.

Decomposition Method
Given that household consumption identity in (1) above depends on household income per capita, following Barros et al. (2006) we re-write income per capita as the product of the share of adults in the household ( ) and income per adult. Income per adult can be rewritten as the sum of labor and non-labor incomes per adult. Labor income per adult is just the product of the share of occupied adults ( ) and the labor income per occupied adult (Box 1, see Annex 1 for details). As a final step, we can then relate household consumption per capita to household income per capita as follows: (2) Since poverty depends on the distribution of consumption across households, it depends on each of the components outlined above. As a result, any poverty (or inequality) measure can be written as a function of each of these components. Therefore, the contribution of each component towards changes in poverty or distribution can be expressed as a function of changes in these indicators between the initial and end periods. Following Barros et al. (2006), we simulate changes in the distribution of welfare by changing each of these components one at a time, to calculate their contribution to the observed changes in poverty.
The result of this analysis is interesting from a policy perspective for various reasons. First, if demographic trends and declining dependency ratios were largely responsible for changes in poverty, population projections can help to distinguish whether this is likely to continue affecting poverty. Second, changes in labor income per occupied person or in the number of adults in the family who are working might explain the importance of work in moving people out of poverty. To the extent that poverty reduction has had more to do with employment and earnings rather than with public social transfers, this may indicate that greater effort should be placed in ensuring that the poor have access to good jobs. Or alternatively, one might question the effectiveness of transfers to redistribute and increase the incomes of the poorest. Third, to the extent that the observed reduction in poverty has been due to international remittances, this would point to the need for more concerted efforts to create employment opportunities domestically. Finally, to the extent that households change their consumption patterns and end 8 up saving a greater share of their income, then we could observe fast income growth but moderate consumption growth.

Box 1. Decomposing Consumption Per Capita a la Barros
It is important to mention a few caveats with these methods from the outset. First, the counterfactual distributions on which these decompositions rely suffer from equilibrium inconsistency. Since we are modifying only one element at a time, the counterfactuals are not the result of an economic equilibrium, but rather a simulation exercise in which we assume that we can modify only one factor at a time and keep everything else constant. Second, as mentioned earlier, these decompositions are path dependent, and as such, sensitive to the order in which the variables are simulated. The best-known way to remedy path dependence is to perform the decomposition across all possible paths and then take the average, also known as the  In other words, one would have to begin with each factor one at a time and follow every possible ordering of factors. To find the results, one would then take the average of the contribution of each factor across all possible paths. Since this grows very quickly with the number of factors, we group the variables into smaller sets, and calculate the Shapley-Shorrocks estimates. 9 We proceed in two steps. First we decompose the observed reduction in poverty into the simplest three elements: the consumption-to-income ratio, the number of adults as a share of the total number of household members and the income per adult. This allows us to explore all possible combinations and paths and to estimate Shapley values (Shapley value decomposition). We then further decompose the observed reduction in poverty by decomposing the elements of the income per adult in each case (Barros decomposition).

Results
The three countries we analyze, Bangladesh, Peru and Thailand, all experienced fast growth and poverty reduction. Panel A in Table 3 show the changes in poverty in the last decade for relevant international poverty rates 11 and the extreme and moderate poverty rates defined by the respective institutes of statistics. Panel B in Table 3 show the results of the most aggregate Shapley value decomposition. The most important contributor to poverty reduction in each country has been growth in income per adult (which captures all labor market outcomes without distinguishing if they are through earnings or more employment plus any non-labor income). Regardless of the decomposition path used, we find that growth in income per adult from all sources explains over 50 percent of the reduction in the Bangladesh poverty headcount using the national moderate and extreme poverty lines, and over 60 percent using the US$1.25 poverty line. Income per adult explains over 85 percent of the reduction in poverty observed in Peru and Thailand, regardless of which poverty line is used ( Figure 8 and Table 3). Changes in the share of adults per household (i.e. the decline in dependency rates) are another important factor behind poverty reduction in Bangladesh and Thailand. Finally, these initial decompositions suggest that if households had continued to consume the same share of income in the final period as what was observed in the initial period, then poverty would have fallen even more in the case of Bangladesh and Thailand. In other words, the fact that households are consuming a smaller share of their incomes in the final period implies that poverty-as measured by consumption aggregates-is higher than if the consumption-to-income ratio had remained constant. This result is particularly important in Thailand. In the case of Peru, by contrast, a higher consumption-toincome ratio contributed to the observed decline in poverty.
Results using different decomposition paths are in most cases invariant to the order in which the decompositions are done. The differences are particularly small in terms of the contribution that income per adult has on observed poverty reduction. 12 These results give us some confidence to further decompose total income per adult into subcomponents using a single path, instead of calculating all potential paths-which would require 5,040 separate decompositions.
To explore the multiple channels behind the changes in poverty depicted in Figure 1, we further disaggregate total income per adult into its subcomponents. The key result that emerges is that 10 the most important contributor to poverty reduction in each country has been improvements in labor market outcomes (Panel C of Table 3). First, more than 70 percent of the poverty reduction can be attributed to rising labor income per adult ( Figure 9). Second, in line with the trends analyzed earlier, the increase in the share of adults per household and the share of occupied adults has also led to a reduction of poverty in Peru (accounting for 18 percent of moderate poverty reduction) and Bangladesh (accounting for 9 percent of moderate poverty reduction). By contrast, the aging population in Thailand led to more adults per household but fewer occupied adults, and therefore contributed to an increase in poverty.
In terms of non-labor income, public and private transfers play a relatively smaller rolebetween 7 and 34 percent-in explaining poverty reduction trends across these countries over the last 10 years. The importance of labor income tends to be lower for lower poverty lines in the case of Peru and Thailand, while the opposite is true for transfers. The finding that transfers are more important to explaining changes in extreme poverty compared to moderate poverty is nontrivial, as it indicates that these public programs are relatively well-targeted to the poorest and have a sizeable impact. But in all cases, the impact is significantly smaller than what is found for labor market outcomes.
The main result that comes out of these decompositions is that labor market-related outcomes have been the main contributor to poverty reduction during the last decade. This is true for moderate poverty lines and even extreme poverty lines in all cases. The next logical question is, what accounts for the increase in total labor income? Was it the result of more people working or higher earnings per worker? Was it the result of changes in occupation or changes in the sectoral composition of employment? Were these changes the result of improved human capital characteristics or higher returns to those characteristics? In order to answer these questions, a more complex model is needed.

An In-Depth Approach
Several potential reasons could explain why labor incomes had an important role in explaining reductions in poverty in these three countries. A look at cross tabulations reveals interesting patterns. First, there were changes in the occupational structure, with workers moving away from farm and daily work and toward salaried employment, which are likely to be economic activities with higher productivity ( Figure 10A). In the case of Peru, there was a shift away from unpaid family employment towards self-employed and salaried work. There was also a sharp shift in employment away from agriculture and towards higher productivity manufacturing and services sectors ( Figure 10B).
Moreover, there has been an improvement in the educational composition of the workforce over the last ten years in each of these countries as a consequence of higher investment in education in previous decades. A smaller share of the population was illiterate at the end of the decade in all countries, a higher share of the workforce had completed primary and lower secondary school in 11 Bangladesh and Thailand and a higher share of the population had completed secondary and tertiary school in Peru and Thailand ( Figure 11A). Finally, there were population shifts across regions, through accelerated urbanization in Bangladesh and Thailand, countries at much lower level of urbanization than Peru ( Figure 11B). In order to distinguish which of these changes has been most important in reducing poverty, a more detailed micro decomposition model is used.

Model
Again we begin with the household consumption identity presented earlier. Consumption per capita in household h is defined by: (1) where n is the number of people in household h, y h is the total income of household h and is the consumption-to-income ratio, which includes the propensity to consume in household h and measurement error or underreporting of household income. If we further disaggregate income by its sources, we can rewrite (1) as: ( 2) where , and are household salaried labor, daily labor 13 and self-employed non-farm labor income respectively, is the farm household net revenue function and is household non-labor income. We slightly modify the Bourguignon and Ferreira (2005) approach and model the household income generating function as: where , and are indicator variables that are equal to one if individual i in household h is a salaried, daily or self-employed worker, , and are the corresponding earnings of individual i in household h that depend on individual and household endowments ( ) and the returns to those endowments ( ), which vary across occupation types. In the rest of the paper we call people earning , and the -non-farm‖ sector, although it includes all dependent workers-including those in agriculture-plus the non-farm self-employed.
is household net revenue in farm activities, which depend on household endowments ( ) and the returns to those endowments ( ). In the rest of the paper, this is the -farm‖ sector. Finally, is household non-labor income.
The allocation of individuals across occupations is modeled through a multinomial logit model (McFadden 1974a(McFadden , 1974b, specified as follows: where is a vector of characteristics specific to individual i and household h, are vectors of coefficients for the following activities j={salaried, daily worker, non-farm self-employed, not employed} and are random variables identically and independently distributed across individuals and activities according to the law of extreme values. 14 Within a discrete utilitymaximizing framework, is interpreted as the utility associated with activity s, with being the unobserved utility determinants of activity s and the utility of inactivity being arbitrarily set to 0. Following Bourguignon, Ferreira and Leite (2008), we estimate a multinomial logit model for the educational choice and sector in which individuals are employed. This allows for a representation of the occupational, sectoral and educational composition of the workforce.
We model the heterogeneity in individual earnings in each occupation type j by a log-linear Mincer model: and j = {salaried, daily worker, non-farm self-employed, not employed}.
is a vector of individual characteristics, a vector of coefficients and a random variable supposed to be distributed identically and independently across individuals, according to the standard normal law. Farm net revenue is modeled as: where include endowments and household characteristics. As before, are vectors of coefficients and are random variables distributed as a standard normal. 13

Implementation
The objective of this model is to distinguish the importance of changes in earnings due to changes in educational attainment, age, gender, occupation, sector and geographical distribution of the labor force. We implement the decomposition in four stages. First, we estimate the determinants of level of education for all individuals, as well as the sectoral and occupational choice for non-farm workers and for the secondary occupation of farm workers for two periods during the last decade. Second, we estimate the earnings regressions for each period for household heads and other household members, distinguishing between salaried, self-employed and daily workers, and for net farm revenue for farm households. Third, we use the coefficients from these regressions to simulate counterfactual distributions by moving one element at a time. Finally, we compare these counterfactuals to the observed changes in distribution in order to identify the contribution to changes in poverty.
We first estimate the education, occupation and sectoral choice models for each period for which data are available. Tables 4 and 5 present comparisons of simulated educational, occupation and economic sector structures using these regressions with the actual structures during the early and late part of the decade for household heads and other family members, respectively. In general, the simulated structures are close to the observed ones. However in some instances there are discrepancies. For instance, the simulated 2010 non-farm occupational structure in Bangladesh has slightly fewer salaried and more daily workers than the true values. In the case of Thailand the simulations underestimate the share of illiterate workers, overestimate the share of agriculture workers and underestimate the share of public sector workers. With the exception of Thailand, the simulated (predicted) structures are close to their true structures as shown by the Pearson Chi-squared test, 15 which gives confidence that we can use the coefficients from these regressions to simulate shifts in the labor force structure on at a time.
Tables A1-A3 in the appendix present the multinomial logit regression results for occupational choice. 16 The regression results show coefficients with the expected signs and a reasonable pseudo R 2 . Given the considerable diversification of the sources of income that is common in rural households, 17 we estimate the sectoral choice model for the secondary occupation of individuals in farm households as well as for all non-farm work. 18 Tables A4-A6 in the appendix present the earnings equation estimates for individuals engaged in non-farm activities. The results show that the models fit the data relatively well, with coefficients being statistically significant and of the right sign. In all cases, higher individual earnings are associated with being male, having higher education and experience, living in urban areas and 14 working in the manufacturing sector. Tables A7-A9 present regression results for farm household net revenue functions. 19 Net revenue for farmers increases with experience, land holdings, access to irrigation and the number of members participating in farm work. 20 The next step consists in using the estimated coefficients from these models to simulate counterfactual distributions. For instance, since we estimated the returns to education in two periods, we can take the estimated parameters in the first period and evaluate the earnings equations with the 2010 levels of education. This generates counterfactual earnings at the individual level, which can then be aggregated to get the corresponding household income using equation (3), which can then be used to get to a counterfactual level of consumption according to (1), and therefore a counterfactual poverty rate. In this way, changing one set of parameters at a time or one characteristic at a time, we obtain multiple counterfactual distributions and counterfactual poverty rates. The methodology for estimating each counterfactual distribution and the associated counterfactual poverty rate is detailed in Annex 2.
Finally, we compare these counterfactual poverty rates with the observed poverty rates to quantify the impact of each element being considered. Since replacing the first period parameters into last period data will yield results that are different from doing it the other way around, we calculate the counterfactual both ways and then take the average (in line with the literature). We first calculate these effects by changing one element at a time and leaving everything else constant. However, given that changes in multiple factors could have interaction effects, we also calculate the cumulative effect of these decompositions. For this purpose, we follow Bourguignon, Ferreira and Leite (2008), and begin by calculating the effects on poverty of changes in the characteristics of the population, beginning with age and gender, followed by changes in geographical, educational, occupational and sectoral structure of the population. With these results we then calculate changes in farm and non-farm earnings due to changes in the returns to these characteristics, followed by changes in non-labor incomes (first private and then public) and finally changes in the consumption-to-income ratio.

Results
Focusing on the contributions to the reduction of moderate poverty based on national poverty lines, Table 6 presents the results of each counterfactual distribution when simulating only one element at a time, and keeping everything else constant. We refer to these as the marginal contributions to poverty reduction. The main result that emerges is that the largest contributions to moderate poverty reduction in all three countries came from labor market-related factors: 61 percent in Bangladesh, 75 percent in Peru and 65 percent in Thailand. Within this, it was the increase in the returns to endowments or characteristics, rather than changes in these endowments or characteristics, that explain poverty reduction, pointing to an increase in real 15 wages and higher productivity as the main contributors to poverty reduction in each case (Tables  6 and 8). While increases in farm income were mostly responsible for poverty reduction in Bangladesh and Thailand, non-farm income was mostly responsible in the case of Peru (Table 6). Finally, while non-labor income played an important role in Thailand and Peru, the results presented here continue to reflect the fact that labor income, either from farm or non-farm sources, was the main contributor to poverty reduction. These main results are complemented by those in Table 7, which presents the contributions of each endowment and the returns to each one of those endowments.
Finally, since each change in endowment or characteristic is likely to be related with every other characteristic, we also compute the cumulative effect of each of these endowments in order to capture the interactions between each of the endowments, following Bourguignon, Ferreira and Leite (2008). Again, the main result that emerges is that the returns to endowments or characteristics were the largest contributors to poverty reduction in all three countries (Table 8).
We look at these results in turn.

Occupation
Changes in the occupational structure were critical for poverty reduction in all countries for nonfarm workers, pointing to shifts in employment as workers aimed to benefit from better work opportunities. This effect was most important in the case of Peru, where the shift in occupation from unpaid family workers into wage employment accounts for 21 percent of poverty reduction (Table 6). In the non-farm sector in Bangladesh, the shift from daily and self-employed work towards salaried employment contributed 9 percent of the observed poverty reduction. 21 In contrast, changes in occupation for self-employed farmers had a negative impact on poverty, reflecting the fact that they were less likely to diversify into a secondary occupation, either because the returns to farm activities increased or because they lacked the skills to do so. For example, we calculated that Thai farmers with a secondary occupation declined from 32 to 23 percent between 2000 and 2009, while in Bangladesh the number of farmers with a secondary occupation fell from 30 to 10 percent between 2000 and 2010. This lower diversification resulted in a 10 and 3 percent increase in poverty in Thailand and Bangladesh respectively, as shown by the contribution of occupational choice in the farm sector (Table 6). 22

Education and Experience
As would be expected, a more educated population helped to reduce poverty in all three countries, particularly in the non-farm sector (Table 7). In Thailand, wage premiums for education increased in both farm and non-farm households, so that the total contribution to poverty reduction on account of a better education amounted to 26 percent of the observed poverty reduction during the period. In contrast, the increase in educational attainment led to only a slight reduction in poverty in the non-farm sector in Peru and Bangladesh (as seen by the effect of changes in endowments); but this effect is countered by the decline in the educational premium, implying that the demand for more educated workers did not keep up with supply. However, the results also point to the fact that the incomes of the unskilled increased relatively faster in Bangladesh and Peru, contributing to poverty reduction (which we see in the constant). Therefore, while a more educated labor force deriving higher earnings made an important contribution to poverty reduction in Thailand, in the case of Peru and Bangladesh the rising incomes of the unskilled made a difference. 23 These results point to greater demand for specialized workers in the case of Thailand compared to Bangladesh and Peru.
Similarly, the returns to greater experience, proxied by age, fell in all cases (Table 7). This effectively means that the incomes of inexperienced, young workers increased relatively faster in Bangladesh and Peru, both in the farm and in the non-farm sector, which contributed to poverty reduction. In contrast, more average experience led to a reduction in poverty in Thailand, both due to greater share of working age population and due to a higher return to experienced workers.
For Bangladesh and Peru, these results point to the fact that there was a relative increase in earnings for workers with less education and experience, which strongly contributed to poverty reduction. In the case of Peru, this is consistent with recent evidence of reductions in returns to education and experience, which also had some impact in the reduction in inequality observed in the end of the 2000s (Jaramillo and Saavedra, 2011). Note that this effect is in part captured by a large contribution to poverty reduction in the constant, which includes the returns to labor for individuals with no schooling, the omitted category (Table 7). This implies that educational increases in the population have been faster than the rate at which job creation was able to absorb them. However, it also points to an important increase in the relative price of unskilled labor, which could at least partly be driven by higher productivity.

Sector of Work
Changes in the sector of work also mattered for poverty reduction, particularly shifts away from agriculture and into services. Panel B in Table 7 shows the impact on poverty of changing sectors within the non-farm sector (from salaried agriculture to services and manufacturing) and the impact of changing sectors in the secondary occupation for the farm sector. In both Bangladesh and Thailand, these effects were more than offset by reductions in the returns to working in those sectors. For instance, in the non-farm sector in Bangladesh, the shift into the service sector accounted for 3 percent of the observed poverty reduction. However, this was more than offset by a reduction the service sector wage premium, leading to a much higher poverty rate than would have otherwise been expected. Similarly, the movement into manufacturing and services in Thailand accounted for 9 percent of the reduction in poverty coming from farm households and 8 percent coming from non-farm households. However, these effects were countered by a decline in returns to working in those sectors, which led to a net increase in poverty. In contrast, despite the increasing share of workers in Peru's service sector, there were increases in returns to working in the service sector, which accounted for 9 percent of the reduction in poverty. This is astonishing, given that the share of service sector workers in Peru is much larger than in either of the other countries (see Table 2).

Regional Structure
One consistent result in all three countries is that the earnings penalty for living outside of the capital city (noted by the region dummy) fell over the last decade, pointing to an increase in real wages and/or higher productivity outside the main capital cities, which helped to reduce poverty. This is most evident in Peru, where the penalty for living outside of Lima declined, accounting for 31 percent of the reduction in poverty, mostly related to a smaller penalty in non-farm activities (Table 7). 24 In Bangladesh and Thailand, the penalty for living outside of the capital also declined, accounting for 15 percent of the reduction in poverty in each case (Table 7), despite the fact that the share of people living outside the capital remained more or less constant.

Rural Assets
There is also some evidence of increased returns to agriculture among farm households in Bangladesh and Peru. In particular, for farm households in Bangladesh, the most important change was the increase in returns to land, accounting for 42 percent of the reduction in poverty (Table 7). This is partly due to land becoming scarcer, as the average land size per capita declined from 0.8 to 0.6 acres per capita between 2000 and 2010. In contrast, the increase in the returns to land in Peru-where the average land size for farm households grew-accounted for 20 percent of the reduction in poverty.
This was complemented by better access to irrigation in the case of Peru, which accounted for 1 percent of the reduction in poverty. In Bangladesh, both access to irrigation and the number of workers in agriculture increased over the course of the decade, while the returns to irrigation and having additional household members employed in farming fell so that neither of these effects helped to reduce poverty.
It is important to mention that we cannot disentangle what fraction of the increase in returns to rural assets is due to an increase in real productivity (real output per worker) or due to an increase in relative prices. Indeed these returns measure the value of the marginal product, which is the product of changes in prices and quantities. Given that this period was characterized by an increase in the relative domestic prices of agricultural products, 25 this factor might have been an important driver of agricultural returns during the latter half of the decade, through its effect on the real value of agricultural production.

Non-labor Income
Changes in non-labor income had a very small role in explaining changes in poverty in Bangladesh, and a larger one in Peru and Thailand (Table 6). In Bangladesh, the increase in international remittances contributed 11 percent to the decline in poverty, but this effect was countered by a decline in domestic transfers, which led to a slightly higher poverty rate than if they had remained constant. Public transfers in Bangladesh increased from 0.9 percent to 1.9 percent of GDP between 2004 and 2010; however they had no impact on poverty reduction (Table 6). This is not surprising given that errors of inclusion are large and the expansion observed since 2004 has been larger among the non-poor (World Bank, 2012b). Moreover, only 34 percent of the poor receive any transfer and the amounts transferred by any of the programs is too small to have a significant impact on poverty.
In Peru, private transfers and donations accounted for 5 percent of the reduction in poverty, while public transfers and donations amounted to 9 percent, not negligible but much smaller than the role played by labor market factors. Conditional cash transfers, in kind transfer programs and social pensions in Peru are expanding, but coverage of these programs was still too small in 2010 to have made a significant impact on poverty.
In Thailand, growth in non-labor incomes was important in explaining reductions in poverty. This is particularly the case for pensions (possibly reflecting the introduction of the new pension scheme), which accounted for 20 percent of the reduction in poverty. Private transfers accounted for another 26 percent of poverty reduction (Table 6). These results are consistent with those using the simple approach, but have been further disaggregated to show the relative importance of the different sources.

Final Remarks
The last decade affords us a fantastic opportunity to study the most significant factors that were at work in favor of the poor. This paper has sought to account for the contributions of different factors to the very sharp reduction in monetary poverty that occurred in Thailand, Peru and Bangladesh-three countries with different levels of GDP per capita, urbanization, share of agriculture, employment patterns, social spending and reliance on remittances. In contrast to methods that focus on aggregate summary statistics, the methods adopted in this paper generate entire counterfactual distributions, allowing us to identify the contributions of various factors to the observed distributional changes and, in particular, to poverty.
The results show that in these three very different settings, the most important contributor to poverty reduction over the last decade has been the growth in labor income. In particular, growth in farm income has been critical in both Bangladesh and Thailand, while growth in the non-farm sector has been more important in the case of Peru.
In all cases, the observed growth in incomes was mainly due to higher returns to endowments: land and experience in the case of Bangladesh, nonfarm work in Peru, and education and experience in the case of Thailand. In each case the results signal an increase in the marginal value of work, either due to increases in productivity or higher real wages. In both Bangladesh and Peru, labor incomes of the poor, those in agriculture and those who were less educated all increased. In contrast, greater specialization and higher returns to human capital seem to have boosted the marginal value of work in Thailand, potentially through productivity increases.
One consistent result in all three countries is that the earnings penalty for living outside of the capital city fell over the last decade, which contributed to reducing poverty. A second consistent result is that each of these countries saw a shift in occupational choice into paid employment, away from daily and agricultural work, and towards salaried jobs, all of which contributed to poverty reduction, particularly in Peru.
Beyond the effects of labor income growth, both methods adopted in this paper showed that an increase in the number of adults per family and the number of them occupied helped to reduce poverty, particularly in the case of Bangladesh and to a lesser extent in Peru. International remittances also helped to reduce poverty in Bangladesh. Finally, transfers played a significant albeit smaller role in the observed poverty reduction in all three countries. In the case of Bangladesh, leakages and small size of individual transfers made their impact on poverty negligible, despite an expansion of transfers programs during the last decade. In Peru, the recent expansion in social expenditures and transfer programs had only a small impact on moderate poverty, but were relatively more important for extreme poverty. A larger impact of public transfers is found in Thailand, mostly related to the expansion of public pension programs. In general, public transfers had a larger role at lower poverty lines, but even there the impact of labor market outcomes in explaining changes in poverty were larger.
These results imply that jobs are responsible for moving the majority of people out of poverty. Job creation, higher productivity and growth in real wages at the bottom of the distribution are the main mechanisms to achieve sustained poverty reduction. Transfers, on the other hand, are especially important for the extreme poor.              Contribution to national moderate poverty reduction on account of changes in:

Annex 1. Decomposing the changes in poverty a la Barros et al (2006)
In order to decompose the contribution of each factor to poverty reduction, we need some structure that would allow us to measure the contribution of each factor to the total change in poverty. We begin following Barros et al (2006), and model household per capita income as: (1) Income per capita is the sum of each individual's income and will depend on the number of household members, n. If in addition we recognize that only individuals older than age 15 contribute to family income, income per capita will in fact depend on the number of adults in the family, , therefore income per capita can be written as: ( 2) Income per adult, in turn, depends on labor income, , and non-labor income, , where nonlabor income includes public social transfers, pensions, remittances and other private transfers.
(3) Finally, recognizing that not all adults in the household are employed, we note that household labor income per capita depends on the income of employed adults. Therefore we can decompose the labor income per employed adult as: (4) where is the number of occupied adults.
In some countries, official poverty rates are calculated on the basis of household income, so equation (4) is sufficient to decompose the contribution of demographic factors, labor and non-labor incomes towards observed poverty reduction. However, most countries measure the distribution of welfare, and poverty in particular using household consumption. Therefore, we modify the Barros et al (2006) approach by mapping consumption to income. In particular, we construct a household consumption model, where household consumption is defined by: (5) where is household income, combines the marginal propensity to consume in household h, and measurement error or underreporting of household income, where , and F(.) is the observed empirical distribution.
Combining (4) and (5) above, we can express household consumption per capita as:

Measuring the Contributions to Poverty Reduction
The basic notion behind calculating the contributions to poverty reduction comes from the realization that poverty measurement depends on the distribution of the welfare aggregate (either income or consumption) across households. More specifically, let F(.) be the cumulative density function of the distribution of welfare. This density function will depend on either income or consumption, and therefore on each of the components outlined above. Since poverty rates depend on F(.), then we can decompose household consumption in each household by the factors in equation (6). As a result, any poverty or inequality measure can be written as a function of each of these components. Therefore the contribution of each component towards changes in poverty or distribution can be expressed as a function of these indicators in the initial and end periods.
Following Barros et al (2006), we can then simulate the distribution of welfare by changing each of these components one at a time, to calculate their contribution to the observed changes in poverty or inequality. In particular, let be a measure of poverty or inequality. Then, this measure will be a function of the cumulative density function, F(.), which in turn depends on each of the factors above: where and Given that the distribution of per capita consumption for period 0 and period 1 are known, we can construct counterfactual distributions for period 1 by substituting the observed level of the indicators in period 0, one at a time. For each counterfactual distribution, we can compute the poverty and inequality measures, and interpret those counterfactuals as the poverty/inequality that would have prevailed in the absence of a change in that indicator. For example, to see the impact of the change in the share of occupied adults, we can compute , where we substitute the value of observed in period 0 to the observed distribution in period 1. We can then compute: Such that the contribution of the share of occupied adults is the difference between the observed in period 1 and the estimated counterfactual, . Similarly, each of the other components in the consumption per capita distribution in period 1 can be substituted by their values in period 0 so that their contribution to changes in poverty can be computed.
Since panel data are not available, we follow the methodology proposed by Juhn, Murphy and Pierce (1993) to assign characteristics from the first period onto the second. More specifically, we first order households along the welfare distribution in each period and divide them into quantiles 26 . We then take the average value of the characteristic for each quantile in period 0 and assign it to each household in that same quantile in period 1. For example, if we are decomposing the effect of labor income, we order households into quantiles by their observed labor income in periods 0 and 1. Then for every quantile in period 1, we replace the period 1 labor income with the average labor income in period 0 from households who were in the same quantile. Barros et al (2006) compute each counterfactual simulation in a nested fashion (as shown in Figure 9 and Table A1). They identify the contribution that interactions between variables have in poverty reduction by first computing the joint impact of a subset of variables, and then subtracting the marginal impact of each variable at a time. For instance, in step 2 in Table 1, they first compute the joint impact of inserting both the share of adults and the income per adult from the first period into the distribution of the second period. They then compute the impact of only changing the share of adults, and take the difference of these two simulations to approximate the marginal impact that changing the share of adults had on the distribution. However, in step 4, instead of computing the impact of income per adult on its own, they compute the impact of changing both the labor and non-labor income per adult. This is done because in principle, the sum of labor and non-labor income should be equivalent to changing total income per adult. However, the results of these two simulations are different. Moreover, the simulation of labor income is not done explicitly, but rather ends up being a -residual‖ in step 8, to ensure that the cumulative effect adds up to the total distributional change.

4.
Contribution of the interaction between labor and nonlabor income is .

5.
Contribution of non-labor income is .

6.
Contribution of the interaction between labor income and the share of occupied adults is .

7.
Contribution of the share of occupied adults is .

8.
Final poverty rate, . The contribution of labor income, , is calculated as a residual: . In contrast, we compute a cumulative counterfactual distribution by adding one variable at a time. The impact of changes in each variable and its interactions with all other variables is calculated as the difference between the cumulative counterfactuals (Table A2). In contrast to the Barros et al (2006) approach, this method does not separately identify the contribution of the interaction between variables on poverty reduction, since doing so is partial at best given that changing any variable can potentially affect all other variables. Moreover, the approach adopted in this paper has the advantage that it avoids attributing the residual to the last variable being considered and allows for a more straight-forward interpretation of the results. The order in which the cumulative effects are built up matter, as described below, so we adopt an ordering that follows a loose hierarchy, in which household demographic characteristics are defined first, followed by labor supply decisions, labor and then non-labor income. This ordering is consistent with the literature on transitions into and out of poverty 27 , and is akin to a VAR structure in the macroeconometrics literature. Finally, as shown in step 2 in Table 2, this approach includes the contribution of changes in the consumption-to-income ratio as part of the decomposition, since the welfare measure is based on consumption rather than income. Contribution of the consumption-to-income ratio is 3.

4.
Contribution of the share of occupied adults is

5.
Contribution of labor income is 6.

7.
Final poverty rate. The unexplained portion is identified separately.

Annex 2. Decomposing the changes in poverty a la Bourguignon, Ferreira and Lustig (2005)
Given the model presented in equations (1) -(6), there are two important steps to get results for the decompositions. The first consists on defining the estimation strategy with the purpose of obtaining a set of parameters for the reduced-form model. The second is the decomposition based on the construction of approximated counterfactual distributions.

A. ESTIMATION STRATEGY
The reduced-form models established earlier require the estimation of different sets of parameters, ranging from the occupational choice model, the educational and economic sector conditional distributions, and (random) estimates of the residual terms. This subsection presents the estimation strategy which has been applied.

1-Occupational choice model: non-farm workers and farm workers
As described earlier, the allocation of individuals across occupations is represented through a multinomial logit model (McFadden 1974a(McFadden , 1974b, specified as follows: where is a vector of characteristics specific to individual i and household h, are vectors of coefficients, for the following activities j={salaried, daily worker, self-employed, not employed}, and are random variables identically and independently distributed across individuals and activities according to the law of extreme values. Within a discrete utility-maximizing framework, is interpreted as the utility associated with activity s, with being the unobserved utility determinants of activity s and the utility of inactivity being arbitrarily set to 0. In order to calculate the utility of activity s and therefore allow for people to change occupations in the simulation exercise when either or change, we must estimate the residual terms of the occupational choice model ( , which are unobserved. They must be drawn from extreme value distributions in a way that is consistent with observed occupational choices. Train and Wilson (2008) Calculating the inverse of this distribution: where  is a draw from a uniform distribution between 0 and 1. Error terms for other alternatives ) 0 (  j with v j hi must be calculated conditioned on the error terms of the alternative chosen ( 0 hi v ). The distribution for these errors is: The inverse of this distribution is: where  is a draw from a uniform distribution between 0 and 1. We repeat this same method when an alternative other than zero is chosen and using expressions (a) and (b).
In the case of farm workers we estimate a model for the secondary occupation in order to capture the probability of diversifying or not into other nonfarm activities. We assume that the residuals are independently and identically distributed according to a logistic function, a logit model is the estimator of the diversification choice to having a secondary occupation or not, for all household heads self-employed in agriculture. The vector of characteristics includes individual and household variables such as age, gender, education level, region and areas among others. Random terms are drawn conditional on the choice that has been made at the initial point.

2-Earning equations: the non-farm and farm workers
Turning to the labor market determination of earnings, we separate the sample into two different groups depending on the kind of activities that these individuals perform: non-farm and farm workers. Individual earnings equations for the first group are estimated separately for household heads, spouses and other members if they are performing as daily workers, self-employed and salaried. The set of characteristics considered in the specification includes individual characteristics such as age, gender, education level, among others as well as characteristics of other members of the household. For instance, in the case of spouses and other members, characteristics of the household head i.e. his level of education; if she is employed or not; etc, were included in the specification. The second step corresponds to estimate the residual terms as random numbers normally distributed and their variances.
As mentioned before, farm net revenues are modeled at the household level and parameters are estimated using ordinary least squares. The vector of characteristics includes endowments such as land and irrigation, and individual and household characteristics of the household head, for instance, educational level, gender, civil status, and number of members involved in the farm activity among others. Random estimates of the residual terms are drawn from a standard normal distribution. Earnings from the secondary occupation are estimated only for farm workers as a function of their individual characteristics i.e. age, gender, education level and economic sector where they perform their secondary job as well as we add a random term distributed according to the normal standard distribution.

3-Other characteristics: educational structure and economic sectors for the main occupation
Since we do not have panel data, we do not observe the same individuals in both years. Hence, to find the contribution of changes in education and economic sector it is necessary to simulate the distribution of these characteristics in year s and apply these coefficients to the population in year t. We estimate conditional distributions of levels of education and economic sectors by occupation categories for each year based on individual age group, gender, region and area. Following Bourguignon, Ferreira and Leite (2008), this is done using multinomial models. These models are estimated separately for household heads, spouses and other members within the working age population.

4-Non-labor income and Consumption-income ratio
We estimate non-parametrically the conditional distribution of all non-labor incomes, both as a total as well as by their different components such as remittances, public transfers and other private transfers. For this purpose, we create cells of household heads with the same level of education, gender and region (urban-rural). Inside of each cell, we create quantiles of non-labor income, we will then ascribe the mean value of each non-labor income component in each quantile/cell in period s, to its counterpart in period t. A similar approach is employed for estimating the conditional distribution of the consumption-income ratio.

B. DECOMPOSITION APPROACH
After each of these reduced-form models has been estimated for two years t and s (early 2000 and late 2010) for each country (Bangladesh, Peru and Thailand), we decompose distributional changes by formulating the appropriate counterfactual distribution of income and consumption. We first estimate the following components of household income at time t and s as explained before as: (7) Which for simplicity we express as: = non-labor income distribution.
We describe first the marginal decomposition technique which consists in changing one component of the distribution at a time, keeping everything else constant. Lastly, we briefly discuss the cumulative approach.

Changes in distribution due to changes in returns to endowments
We can simulate the counterfactual household income distribution by computing the earnings of every household at time t with the estimated returns to individual and household characteristics ( ) computed for period s. 28 This simulation yields the earnings of each household in the sample if the returns to each observed characteristics had been those observed at time s rather than the actual returns observed at time t, keeping everything else constant. 29 The contribution to the overall change in the distribution assigned to a change in returns ( ) between t and s, leaving everything else constant, can be obtained by comparing (8) with (9). However, in this paper we focus on comparing poverty indicators . Therefore, the effect of a change in returns on poverty change is: The difference between this simulated distribution of household incomes and the actual distribution is equivalent to the price effect in the Oaxaca-Blinder calculation. 28 The notation refers to estimating earnings in period t using the returns to characteristics, estimated at time s. 29 The returns to the unobserved characteristics behind the residual term are assumed to be unchanged.

Changes in distribution due to changes in unobservable factors
To simulate the effect of changes in unobservable factors between s and t, we rescale the estimated residuals of the earning and net revenue equations for non-farm and farm workers of time t by the ratio of standard deviations at time s and t. This counterfactual is defined as: Again the contribution to the change in poverty assigned to a change in unobservable factors ( ) between t and s, leaving everything else constant, can be obtained by comparing the actual distribution (8) with the counterfactual (10).

Changes in distribution due to changes in occupation, education structure and economic sectors
Whenever the coefficients of the occupational, educational or sectoral multinomial logit model of year t are replaced for those of year s, individuals may be reallocated into different occupations, education levels or economic sectors. 30 Labor income is imputed to account for these changes using the earnings equations as a linear projection with the relevant vector of parameters and the residuals drawn from a standard normal distribution.
For instance, the contribution to the change in poverty between t and s is calculated by first exchanging parameters for in the occupational choice model, maintaining everything else constant, and then obtaining the following counterfactual distribution: This result can be compared to the actual distribution in (9). We calculate poverty indices for both distributions and take the difference between them to find the contribution to poverty reduction: Note this example refers to the main occupation structure for individuals in the non-farm sector. In the case of the education structure we change parameters with in the function. However, since education has effects on occupation and earnings, it affects each of these functions ( , O and F) and we obtain a counterfactual distribution such as: (12) Once again, the contribution of the change in education structure to the change in poverty between t and s can be estimated by the difference between poverty indices of actual (equation (9)) and counterfactual distribution (equation (12)): For sector of work, we change parameters with in the function. Since sector has effects only on earnings, if affects only the NF and F equations. We obtain the counterfactual distribution as follows: (13) The difference between the distribution of this set of simulated incomes and the actual set of incomes of period t is comparable to the endowment effect in the Oaxaca-Blinder decomposition.

Changes in distribution due to changes in demographics
The next decomposition consists of altering the joint distribution of exogenous household characteristics such as age, gender, region and area of each individual in the household. These variables do not depend on other exogenous variables in the model; the simulation is performed simply by recalibrating the population by the weights corresponding to the joint distribution of these attributes in the target year. Formally, and the contribution to poverty change will be:

Changes in distribution due to changes in non-labor income & consumption-income ratio
The conditional distributions estimated in the previous step are used for the rank-preserving transformation of the observed distribution of non-labor income in each year. In particular, we created cells of household heads with the same level of education, gender and region (urbanrural). Inside of each cell, we created quantiles of non-labor income. We estimate the counterfactual distribution of non-labor income in year t by assigning the mean value of non-labor income of quantile q in cell c in year s, to the same quantile and cell in year t. In other words, we ranked the two distributions by per capita household non-labor income and if q was the rank of household with income at time t, we replace it with the non-labor income of the household with the same rank at time s. We apply the same decomposition methodology for the case of the consumption-income ratio.
For the non-labor income, the counterfactual distribution could be expressed formally as: As before, we can compare with the actual distribution described in equation (9), calculate poverty indices and obtain the contribution of non-labor income to poverty change between years t and s: It is important to note that all previous decompositions are also performed both considering s as the initial year and then considering t as base year. The average of these marginal effects decompositions is the final result reported in the analysis. 31

The Cumulative decomposition technique
As mentioned before, there could be interaction effects between each of the marginal effects considered above. The cumulative decomposition technique allows us to account for these interactions by calculating each effect and successively and cumulating into counterfactuals that contain the cumulative effects of multiple changes. We attribute all of the additional contribution to poverty change to each specific factor being added. However, the magnitude of that contribution will depend on the path chosen for the decomposition. 32 We follow the Bourguignon, Ferreira and Leite (2008) approach by first calculating the effects of changes in the characteristics of the population, beginning with the exogenous variables such as age, gender, region and area ( . Formally, Second, keeping the demographic effects, we add the education structure change ( : Third, preserving the previous changes, we include the change in occupation structure ( : Fourth, we add the change in the structure of economic sectors ( :: Fifth, we include the returns to non-farm sector ( Then we change the returns to farm sector ( Next, we change residuals of earnings and net revenues equations: Finally, we add the change in non-labor income components and the consumption ratio. The latter is not formally displayed in this example: Again, this cumulative decomposition technique is also performed both considering s as the initial year and then considering t as the initial year. The average of these decomposition effects is the final result reported in the analysis.
Lastly, it is relevant to clarify that even we decompose these changes sequentially; it is still possible to have an unexplained portion, both because the sum of the average contributions does not necessarily lead to the total change in distribution and because there may be other factors that contributed to distributional changes that were not considered in the analysis. This residual term is relatively small, implying that either the factors not included are not extremely important or they tend to compensate for each other.         6.248*** 6.709*** 5.268*** 5.133*** 5.813*** 5.949*** 6.495*** 6.764*** 5.462*** 5.114*** 5.992*** 5.530*** (0