In this section of the Help system, we discuss how growth, inequality, and population are the proximate drivers of poverty. We devote very limited attention to population, because growth and inequality determine the rate of poverty; population then determines the number in poverty.
The connection between growth, inequality and poverty
Inequality (the distribution of income or consumption), growth, and poverty form the three vertices of a “triangle”, arithmetically connected in a fairly straightforward way (Bourguignon, 2004). In order to understand this connection, we first discuss the representation and characterization of inequality.
The Lorenz curve is the most widely-used method for representing inequality in earnings, income, or wealth (see the figure below). It portrays the cumulative share of income (or any other quantity distributed across a population) held by increasingly well-to-do cumulative shares of population. The more equally distributed a factor is, the closer the Lorenz curve will be to the hypotenuse of the right-triangle, sometimes called the line of equality. The Gini coefficient is the “area of inequality” immediately below the hypotenuse (A) divided by the area of the triangle (A+B); thus larger Gini coefficients indicate greater inequality.
The Lorenz curve is “non-parametric” in the sense that it is an empirical distribution that is an accurate representation of survey data on income or consumption for a society. While the Lorenz curve is useful conceptually, to capture the dynamically evolving distribution of income or consumption it is more convenient to have an analytic or “parametric” representation of the distribution. Moreover, we want a representation from which we can conveniently compute specific deciles or quintiles (thereby reconstructing the Lorenz curve) and also compute key poverty measures like the headcount.
The most widely-used parametric representation is the lognormal density. A density curve captures the percentage of the population that earns or consumes a given amount (unlike a distribution that captures the cumulative percentage of population that earns or consumes up to a given amount). Although income and consumption are not exactly distributed in a lognormal form for every country, it is a very good approximation to observed empirical distributions. As Bourguignon (2003: 7) notes, a lognormal distribution is “a standard approximation of empirical distributions in the applied literature.” A variable is lognormally distributed if the natural logarithm of that variable is normally distributed, as in the well-known “bell curve.” The next figure shows a lognormal density curve.
One advantage of using a lognormal density to capture the distribution of income in a society is that it can be fully specified with only two parameters, average income and the standard deviation of it. More useful for our purposes, and as elaborated in the following box, the Gini coefficient can be used in lieu of the standard deviation (An extended discussion is provided here).
The following figure provides an illustration of how to obtain the poverty headcount from a lognormal density curve. For a specified poverty line—for example, the one corresponding to dollar a day—the area to the left of the line gives the poverty headcount ratio. The first vertical line in the figure shows the poverty line, and hatched lines show the area corresponding to the headcount ratio. The poverty headcount number is the headcount ratio times population. The box above provides the formal relationships among income distribution, poverty line and poverty.
The income distribution and population also make possible calculation of the poverty gap and relative poverty. With respect to relative poverty, suppose the poverty line were set at one-third the per capita income. The poverty line would then be drawn at this level instead of the fixed dollar-a-day level. The area to the left would give the proportion of the population living in relative poverty and when multiplied by the population would provide the number of people living in relative poverty.
What is the role played by economic growth—the third vertex of the triangle discussed by Bourguignon (2004)—in calculating poverty? The discussion up to now has focused on calculating poverty at a particular point in time, when the distribution and population are known. Economic growth is related to the evolution of poverty over time.
While economic growth usually refers to the increase of per capita income (the average of the income distribution) over time, the process of growth should be more generally understood as affecting the entire income distribution. The incomes of different segments of the population will grow at potentially different rates. The figure below illustrates how the ensuing change in distribution will affect poverty.
In this figure, the second vertical line shows the distribution for a given point in time, say Year 1. The dashed vertical line shows the distribution for a subsequent time, say Year 2. The two vertical lines together show growth from Year 1 to Year 2 in the per capita income, the average of the respective distributions. The area of hatched, dashed lines to the left of the poverty line in the new distribution shows the new poverty headcount ratio. This area is smaller than the area under the Year 1 distribution, and the poverty headcount ratio has decreased. What happens to the poverty headcount number depends on the how the population has changed between the two years. If the population increases significantly, the headcount number can increase even if the headcount ratio decreases.
In this illustration, economic growth gives rise to a decrease in poverty rate, since the lower tail of the distribution becomes thinner. This need not always happen. In order to understand the effects of growth and distribution on the dynamics of poverty, we need next to decompose poverty changes into growth and distribution effects.
Decomposition of poverty changes into growth and distribution effects
The exact way in which the income or consumption distribution changes over time will clearly affect the poverty numbers. Economic growth increases the mean or per capita income by shifting parts or all of the distribution to the right. If the entire distribution shifts right without changing shape, or changes shape such that the left tail of the distribution becomes thinner, then growth will necessarily reduce poverty for a fixed poverty line. Otherwise, poverty could increase even if the per capita income grows.
Bourguignon (2004: 3) describes a decomposition of changes in poverty into growth and distributional changes as follows (also see, Datt and Ravallion 1992): 
A change in the distribution of income can be decomposed into two effects. First, there is a proportional change in all incomes that leaves the distribution of relative income unchanged, i.e. a growth effect. Second, there is the effect of a change in the distribution of relative incomes, which, by definition, is independent of the mean, i.e. a distributional effect.
What is the evidence on poverty changes arising from the interaction of growth and distributional effects? There is evidence that growth tends to be “distribution neutral” on average; Ravallion and Chen (1997), Ravallion (2001), Dollar and Kraay (2002), find a close to zero correlation between changes in inequality and economic growth. This is consistent with the evidence that the growth effect dominates and growth tends to reduce absolute poverty (World Bank, 1990, 2000, Ravallion, 1995, Ravallion and Chen, 1997, Fields, 2001, and Kraay 2004). World Bank (2001) and Ravallion (2004) suggest that the “elasticity” of the dollar-a-day poverty rate to growth is -2; an increase in the growth rate by 1% is associated with a decrease of 2% in the headcount index of poverty.
While there is general consensus that growth is good for poverty alleviation, a few voices of caution can be heard. The actual reduction in poverty is arguably lower than might be expected given recorded rates of economic growth. This has been termed “the paradox of persistent global poverty” (Cline 2004: 28). Poverty in the 1990s declined by less than would have been predicted with a poverty-growth elasticity of around -2. Khan and Weiss (2006) warn that the elasticity of poverty to growth can vary widely—only -0.7 for the Philippines compared to -2.0 for Thailand—depending on the initial inequality and changes in inequality over time. Ravallion (2004) lists a few reasons to be cautious about the finding of distribution neutrality of growth: measurement error in changes in inequality, possible churning under the surface with winners and losers at all income levels, and possible increases in absolute income disparities. Moreover, a few countries and regions could experience poverty increases from distributional changes, even if on average there is neutrality. 
In addition to uncertainties introduced by income inequality effects, the elasticity approach to anticipating poverty decline with income suffers from a problem that Chapter 2 discussed. A given rate of economic growth will have a bigger impact on poverty headcount when the poor are clustered closely around the poverty line than when their incomes fall markedly below the line. In some countries this phenomenon might explain the weaker than expected response of poverty levels to growth in the face of only modest changes in overall inequality. 
The lognormal approach for forecasting poverty of this volume eliminates the need to use the elasticity approach. In fact, lognormal specifications could be used to calculate variable poverty elasticities across countries and time.
If growth in general reduces poverty, are there certain types of growth patterns that are particularly helpful? The idea of pro-poor growth is at the heart of many a poverty reduction strategy. Ravallion (2004) uses the decomposition of poverty into growth and distribution components to formalize the notion of pro-poor growth. One usage defines growth as pro-poor only if poverty falls by more than it would have if growth were distribution neutral (Baulch and McCullock, 1999, and Kakwani and Pernia, 2000). In other words, pro-poor means that the poor experience higher growth than the non-poor. Policy prescriptions associated with pro-poor growth typically include rapid job creation for the relatively unskilled, public expenditure on infrastructure, health, and education disproportionately oriented towards the poor, and “narrow targeting” measures to provide special support to the poor.
Ravallion and Chen (2003) alternatively define a term called the “distributional correction” as the ratio of actual poverty over time to the poverty that would have resulted under distribution neutrality. If the distribution shifts in favor of the poor this would be greater than one, and if it shifts in favor of the rich it would be less than one. The formulation becomes:
Rate of pro-poor growth = Distributional correction x Ordinary growth rate
Their definition is less restrictive in the sense that the rate of pro-poor growth can be high even if the distributional correction is less than one (distribution shifts in favor of the rich) provided the ordinary growth rate is high enough. They argue this is the right way to measure pro-poor growth if assessing poverty reduction caused by growth is the objective.
 Bourguignon (2004) developed graphics that explain these effects more extensively. Perry et al (2006) and Foster, Greere, and Thorbecke (1984) provided mathematical decomposition.
 Perry et al (2006) pay particular attention to inequality in their examination of poverty in Latin America. They argue that the growth elasticity of poverty decreases (in absolute value) with inequality. Since poverty in richer, more unequal countries is more reactive to changes in inequality, while poverty in poorer, more equal countries is more reactive to changes in growth, different policies might be needed to address poverty. Also see Ravallion (1997, 2001) and Kraay (2004) in this regard.
 Cline (2004) uses this explanation for his ‘cross section paradox’ that poverty levels are higher than expected on the basis of a standard form of income distribution in some of the large higher income countries like China, India, and Mexico. Technically it means that the share of inequality taken by those around the poverty line is greater than would be found in a log normal form of income distribution.