Growth-Inequality Decomposition

(Datt - Ravallion Decomposition)

• Definitions and Concepts
• Limitations 
• Notes / Extensions 
• Quick Results (with ADePT and STATA)
• Data Requirements 
• Helpful Tips 
• Annotated Examples 
• References / Related Papers 

Definitions and Concepts

The growth-inequality decomposition introduced by Datt and Ravallion (1992) quantifies the relative contributions of economic growth and redistribution (e.g., changes in inequality) to changes in poverty. The results can tell us, for instance, whether changes in a welfare distribution have offset gains from economic growth in reducing poverty. With this method, the change in a poverty measure (e.g., headcount index, poverty gap, or poverty gap squared) is decomposed into three components: i) growth, ii) redistribution, and iii) residual:

where t₀ is the initial year of the period, t_n is the final year of the period, and r is the reference year at which the welfare distribution and mean welfare are held fixed for the growth and redistribution components respectively.

The figures above illustrate the growth and redistribution components of a change in poverty. The vertical red line represents the poverty line, so the area under the curve and to the left of the red line represents the share of the population living in poverty. Thus, the change in the headcount poverty index is the area between the initial and final distributions to the left of the poverty line. The growth (redistribution) component of this change is the area between the initial distribution and a theoretical one that holds the distribution constant (the mean constant). Since the sum of these two components will not necessarily equal the actual change in poverty, the residual term will make up the difference.

• The growth component represents the change in poverty attributable to changes in mean welfare (i.e., economic growth) when holding the relative distribution of the reference year constant:

where z is the poverty line, µ is the mean income or expenditure, L is the Lorenz curve, and the other parameters are defined as above. In other words, this is the change in poverty that would have occurred if everyone had experienced the same rate of growth as at the mean and therefore maintained their positions relative to one another (i.e., distribution curve shifts but maintains same shape).

• The redistribution component represents the change in poverty attributable to changes in the distribution curve holding mean welfare constant:

In other words, this is the change in poverty that would have occurred if the observed change in the shape of the welfare distribution curve (i.e., redistribution) had occurred without any shift in the mean of the curve (i.e., no growth).

• The residual, sometimes referred to as the interaction term, represents the effect of simultaneous changes in mean income and distribution on poverty that is not accounted for by the other two components. It is essentially the part that cannot be exclusively attributed to growth or redistribution. When the residual term is not negligible in size, the interpretation of the other components may be questionable. Note that similar decompositions (e.g., Kakwani and Subbarao (1990) and Jain and Tendulkar (1990)) do not include the residual term, implying that it is equal to zero, and is included as part of one or both of the other components.

Limitations

Notes / Extensions

• The common finding (though certainly not universal) is that the growth component of the Datt-Ravallion decomposition accounts for the bulk of the measured changes in poverty. However, from this finding, we cannot assume that inequality is not important for poverty reduction. All this empirical finding tells us is that there was little effective redistribution in favor of the poor.
• It is possible to have a growth component greater than 100% of the change in poverty and a negative redistribution component (e.g., 110% and -10% of the poverty change). In this example, the results would indicate that increasing inequality is partially offsetting the impact of growth on poverty reduction.
• This decomposition can also be used to compare differences in poverty across countries, regions, or sectors. When comparing across countries, per capita income or expenditure and poverty lines should be in PPP terms (i.e., adjusted using PPP deflators) so that the data are comparable. Also, each country (region or sector) should be used as the reference, and each of their poverty lines should be used as well. This means you should run the Stata command twice using different poverty lines. See Datt and Ravallion (1992) for details.
• An extension by Kolenikov and Shorrocks (2005) decomposes variations in poverty across regions into three contributing factors – nominal income, inequality, and poverty line – using decomposition techniques based on the Shapley value in cooperative game theory. In this three way decomposition, the redistribution component is divided into marginal contributions of inequality and poverty line differences. Given the path dependence of the decomposition, this method uses the mean of each of the marginal contributions of each factor (this is the “average effect” in the gidecomposition output). As a result, this method does not have a residual component as in the Datt-Ravallion method. [The STATA program for Shapley decompositions written by Kolenikov is available at http://ideas.repec.org/c/boc/bocode/s411401.html]
• The redistribution component is insensitive to changes in the distribution above the poverty line (i.e, changes to the non-poor).

• Stata:The command “gidecomposition” will perform this decomposition quickly and display the results for both reference points in a single table. The Stata ado file (written by Michael Lokshin and Martin Ravallion) must be installed on your computer for the command to work. See the annotated examples for step-by-step details for installation and the “gidecomposition” command.
• ADePT (Automated DEC Poverty Tables): ADePT is a Stata based software program that automates the economic analysis typical for poverty assessments and produces a package of graphs and tables with standard poverty and inequality statistics or individual outputs a la carte. This decomposition is included in the ADePT Poverty module and results are displayed in Table 3.5. For more details on installation and use, refer to the ADePT User’s Guide and website.

Data Requirements

• 2 or more comparable household surveys
• Per capita (or per adult equivalent) expenditure or income variables should be in real terms (e.g., constant local currency) when decomposing differences across time.
• Poverty line variables (or numbers) also in real terms.
• Survey sampling weights.

Helpful Tips

• If analyzing two or more sub-periods (e.g., 1990-1995 and 1995-2000 as sub-periods of 1990-2000), use the initial year of each sub-period as the reference year. This will allow you to add up the sub-period components and have them equal the decomposition for the entire period.
• You can use the common Foster-Greer-Thorbecke (FGT) poverty measures by specifying “hc”, “pg”, or “pgs” (for headcount, poverty gap, and squared poverty gap, respectively) at the end of the command in Stata.
• Make sure your weights are appropriate. Typically, this is the household level sampling weight times the household size.
• The sectoral (Ravallion and Huppi) decomposition of poverty can complement this growth-inequality decomposition.

Annotated Examples

Here is an example of the growth-inequality decomposition using the Uganda sample data with notes explaining the command line specification and the output. The data sets and variables are defined in the Sample Data section.

Make sure that the gidecomposition command (ado file) is installed on your copy of Stata; see the Installation of Stata ado files section for details.

Example 1

. cd C:\yourdir\yoursubdir [substitute the location where you placed the sample data files]
. use ugahh92, clear [Note: “ugahh92.dta” is the data for the initial year of the period]
. gidecomposition using ugahh02 [aweight=iwe], var1(welfare) var2(welfare) pline1(spline) pline2(spline) hc

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Growth and Inequality Poverty Decomposition
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a) “Base year 1” column uses 1992, the year of the first data set (ugahh92), as the reference year (i.e holding the 1992 Lorenz curve constant for the growth component and the 1992 mean per capita expenditure constant for the redistribution component).

“Base year 2 ” column uses 2002, the year of the second data set (ugahh02), as the reference year.

b) The poverty rates (headcount poverty indexes) are 56.4% and 38.8% for 1992 and 2002, respectively. Verify that the poverty rates in the tables are consistent with other measures of poverty.

c) Change in P0: Poverty fell from 1992 to 2002, and the change is 38.819 – 56.427 = -17.608 percentage points.

d) Growth component: If the Lorenz curve had remained constant as observed in 1992 (2002), the headcount index would have decreased by 25.1 percentage points (26.2 points) during this period of growth.

e) Redistribution component: If mean consumption had remained constant as observed in 1992 (2002), the rise in inequality, that is an increase in the variance of the distribution, would have increased poverty by 8.6 percentage points (7.5 points). In other words, the rise in inequality offset gains from growth in reducing headcount poverty.

f) Interaction component: This is also referred to as the residual term. The results of the decomposition are questionable when this term is not small relative to the change in poverty.

g) Average effect: This column presents the mean of each of the marginal contributions of each factor (i.e. the average of “Base year 1” and “Base year 2” results). Given the path dependence of this decomposition, one may choose to use the mean values (i.e. Shapley decomposition).

Example 2

Instead of decomposing changes in headcount poverty, we can decompose changes in the poverty gap or poverty gap squared by specifying “pg” or “pgs” at the end of the command.

. gidecomposition using ugahh02 [aweight=iwe], var1(welfare) var2(welfare) pline1(spline) pline2(spline) pg

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References / Related Papers

Datt, G. and M. Ravallion (1992). "Growth and Redistribution Components of Changes in Poverty Measures: A Decomposition with Applications to Brazil and India in the 1980s." Journal of Development Economics, 38, 275-295.

(Link above is for Science Direct subscribers. Other versions are available: Living Standards Measurement Study (LSMS) Working Paper No.83)

Jain, L. R. and S. D. Tendulkar (1990). "Role of Growth and Distribution in the Observed Change of Headcount Ratio Measure of Poverty: A Decomposition Exercise for India." Indian Economic Review, 25(2), pp. 165-205.

(Can be ordered from http://www.ierdse.org/)

Kakwani, N. and K. Subbarao (1990). "Rural Poverty and its Alleviation in India." Economic and Political Weekly, 26(24), pp. 1482-1486.

(Link above is for JSTOR subscribers.)

World Bank (2005). Economic Growth in the 1990s: Learning from a Decade of Reform. Washington, DC: The World Bank.

Growth-Inequality Decomposition | Sectoral Poverty Decomposition |
Growth Incidence Curve | Rate of Pro-Poor Growth | Growth Elasticity of Poverty |
Installation of Stata ado files | Sample data

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