Growth Incidence Curve

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

Definitions and Concepts

The growth incidence curve (GIC) plots the growth rate at each quantile of per capita income (or expenditure). The GIC graph can allow us to compare the incidence of growth in poorer segments of the population with that of richer segments or with the rate of growth of mean income (or expenditure).

If we rank the observations in each of our household data sets by per capita income (or expenditure) from poorest to richest, we can use the income (or expenditure) measure for a given quantile p at two different points in time, t and t-1, to calculate the growth rate for quantile p:

Note that this is the basic equation for calculating the growth rate over one period, but instead of calculating it at the mean, we are calculating it at each quantile. If the time period spans more than one year, then the average annual growth rate would have to be calculated accordingly:

where n is the number of periods. Once we have calculated the growth rate at each quantile, it is only a matter of plotting growth rates versus percentile to obtain a growth incidence curve.

Notes / Extensions

To track changes in income of individuals rather than just anonymous segments of a population (i.e. percentiles), Jenkins and Van Kerm (2006) utilize panel data to decompose changes in income inequality into progressivity and mobility components that reflect, respectively, the degree of pro-poor growth and the reranking of individuals in the income distribution.

Quick Results with ADePT or Stata

• Stata: The command “gicurve” will produce a graph of growth rates versus percentile. The Stata ado file (written by Michael Lokshin) must be installed on your computer for the command to work. If a poverty line or headcount measure is specified, the rate of pro-poor growth will also be calculated with this command. See the annotated examples for step-by-step details for installation and the “gicurve” 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. The growth incidence curve can be produced with the ADePT Poverty module. Results are displayed as Figure 2.1. 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 with measures in real terms (e.g., constant local currency).
• Survey sampling weights.
• Optional: Headcount poverty index or poverty line (only 1 number) to calculate rate of pro-poor growth.

Helpful Tips

• If the time period is more than one year, remember to specify the number of years in the period to obtain annual growth rates.
• Since individuals may change their rank in the distribution over time, the individual at say the 25th percentile in the initial year is not necessarily the same individual at the 25th percentile in the final year. So if the incidence of growth is positive for all quantiles of the growth incidence curve, we cannot say that everyone’s welfare (expenditure or income) increased during the period but can say that welfare increased at each quantile or percentile.
• If the Lorenz curve does not change, then the growth rate at each quantile will equal the growth rate of the mean. In this special case, the growth incidence curve would be flat (and equal the growth rate of the mean) implying that growth was distributionally neutral.

Annotated Examples

Here is an example of the growth incidence curve and the rate of pro-poor growth 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 gicurve command (ado file) is installed on your copy of Stata; see the Installation of Stata ado files section for details.

Example 1

We start with a basic specification for the “gicurve” command.
. 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]
. gicurve using ugahh02 [pweight=iwe], var1(welfare) var2(welfare) yperiod(10)[Note: “ugahh02.dta” is the data for the final year of the period]

When a headcount poverty index or poverty line is not specified, a table listing the rate of pro-poor growth corresponding to select percentiles (i.e., headcount poverty rates) is generated. For instance, the rate of pro-poor growth or the mean growth rate for the first 10 percentiles is 3.24.

Example 2

By specifying the headcount poverty index or a poverty line, the corresponding rate of pro-poor growth will be displayed. Since we have regional poverty lines (i.e., more than one poverty line), we will first estimate headcount poverty index (p0) with sepov command in the initial year to use with the gicurve command. Alternatively, we could also refer to the output of our decomposition tables for the headcount poverty index. (Note: the sepov ado file must be installed on your computer; see Installation section.)

. sepov welfare [pweight=iwe], povline(spline) strata(stratum) psu(ea)

Poverty measures for the variable welfare: Consumption per adult equivalent (in constant Uganda shillings)

Survey mean estimation

The estimate for p0 (.5642735) indicates that the headcount poverty index is 56.4%. This is used as a parameter in the command below to calculate the rate of pro-poor growth (enter the command on one line).

. gicurve using ugahh02 [pweight=iwe], var1(welfare) var2(welfare) yperiod(10) [These four lines should be entered as one.]< /EM>
np(200) hcindex(56.43) ginmean ci(500 95)
title("Growth Incidence Curve - Uganda 1992-2002/03") ytitle("Growth rate") [Note: These are standard Stata graph options.]
legend(order(2 "GIC" 3 1 "95% Confidence Interval" ))

In the second line of the command above, np(200) specifies 200 quantiles, hcindex(56.43) specifies the headcount poverty index, ginmean indicates that a horizontal line should be drawn at the growth rate in the mean (i.e., at 4.09), and ci(500 95) specifies that a 95% confidence interval should be estimated through 500 bootstrap replications.

The third and fourth lines above are standard Stata graph options.

Headcount poverty rate in initial year is 56.43.

Note that the rate of pro-poor growth (2.90%) is less than the growth rate in mean (4.09%), indicating that while the poor benefitted from growth, the nonpoor benefitted more. Visually, the graph shows that the growth rate is about 3% for the lower 3/4 of the distribution, whereas the top 10% experienced growth rates of 4-7%.

It is always good practice to include confidence intervals. Notice that confidence intervals tend to be wider at the ends of the distribution, where there are fewer observations.

Example 3

This example calculates the Growth Incidence Curve for 2002/03 – 2005/06.

. cd "C:\yourdir\yoursubdir"
. use ugahh02, clear
. sepov welfare [pweight=iwe], povline(spline) strata(stratum) psu(ea)
 [Note: This calculates headcount index of 38.82; enter this in the next command]
. gicurve using ugahh05 [pweight=iwe], var1(welfare) var2(welfare) yperiod(3)
np(200) hcindex(38.82) ginmean ci(500 95)
title("Growth Incidence Curve - Uganda 2002/03-2005/06") ytitle("Growth rate")
legend(order(2 "GIC" 3 1 "95% Confidence Interval" ))

For the period 2002/03 to 2005/06, the results indicate that growth was pro-poor (rate of pro-poor growth greater than the growth rate in the mean) and benefitted the entire distribution. While growth for the top 5% of the distribution was lower than the rest of the distribution, it was still positive.

References / Related Papers

Ravallion, M. and S. Chen (2003). "Measuring Pro-Poor Growth." Economics Letters 78: 93–99.

(Link above is for Science Direct subscribers. Other versions are available:  World Bank Policy Research Working Paper – No. 2666)

Jenkins, S. and P. Van Kerm, (2006). "Trends in Income Inequality, Pro-Poor Income Growth, and Income Mobility," Oxford Economic Papers, 58(3), pp. 531-548.

(Link above is for Oxford Economic Papers subscribers. Other versions are available: IRISS Working Paper No. 2003-11)

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

Back to Measuring the Growth-Poverty Link