# Estimating the Elasticity of Growth in the US Using the Generalized Means of Income

## Abstract

Economic growth has been a key mantra to promote poverty reduction in developing countries. Studies have shown that a 1 % GDP growth can reduce absolute poverty (or increase the average income of the poorest quintile) by 1 % or more in developing countries. The literature calls this relationship between poverty reduction and growth as growth elasticity. However, there is very little research available studying the extent of growth elasticity in a developed economy. I fill this vacuum in literature by applying the method of generalized means of income outlined in Foster and Székely (Int Econ Rev 49(4):1143–1172, 2008) on micro-level data to estimate the elasticity of growth in the US. The generalized means of income of Foster and Székely (Int Econ Rev 49(4):1143–1172, 2008) satisfies all the axioms of a good income standard, which makes it a preferred method to measure the elasticity of growth. My analysis shows that most of the growth in the US is driven by the richer segment of the society. The ‘wealthier’ poor get some benefit from growth—a 1 % increase in per-capita state-level income leads to about 0.9 % increase in their income both in the short and long-run. However, this relationship diminishes when I calculate the growth elasticity of those in deeper poverty. Sector-wise decomposition of income shows that the ‘wealthier’ poor benefits from an increase in the size of the service sector, but those in deeper poverty do not see this benefit.

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## Notes

1. 1.

$${\text{Growth}}\,{\text{elasticity}} = \frac{{{\text{Percentage}}\,{\text{improvment}}\,{\text{of}}\,{\text{the}}\,{\text{condition}}\,{\text{of}}\,{\text{the}}\,{\text{poor}}\,{\text{in}}\,{\text{country}}\,{\text{i}}\,{\text{at}}\,{\text{time}}\,{\text{t}}}}{{{\text{Economic}}\,{\text{growth}}\,{\text{in}}\,{\text{country}}\,{\text{i}}\,{\text{at}}\,{\text{time}}\,{\text{t}}}}$$.

2. 2.

Number in Poverty and Poverty Rate: 1959 to 2011. US Census Bureau. http://www.census.gov/hhes/www/poverty/data/incpovhlth/2011/Figure4.pdf.

3. 3.

An income standard is a method that summarizes individual income of a population into one single index, without using any kind of poverty line or cutoffs to summarize the income (Foster and Székely 2008).

4. 4.

For example, the World Bank uses \$4 a day poverty line for Latin American countries. http://www.worldbank.org/en/news/press-release/2012/11/13/new-world-bank-report-finds-fifty-percent-increase-middle-class-latin-america-over-last-decade.

5. 5.

“Household Income for States: 2010 and 2011” US Census Bureau. http://www.census.gov/prod/2012pubs/acsbr11-02.pdf.

6. 6.

Equation (2) is slightly different from equation estimated by Foster and Székely (2008). They use the following equation for estimation (Eq. 2 of their paper): $$y_{\alpha ,it} - y_{\alpha ,it - 1} = \gamma + \beta \left( {y_{1,it} - y_{1,it - 1} } \right) + Z'_{it} \theta + \mu_{i} + \tau_{t} + \varepsilon_{it}$$. In their paper, β has a slightly different meaning. It measures how much the generalized means of income increases (in terms of percentage points) if growth rate increases by one percentage point. Nonetheless, in both cases, the β can be used to draw similar conclusions about evolution of income.

7. 7.
8. 8.

I also repeated the robustness tests using lagged value of ln(y1) instead of its contemporaneous value. Although not reported, I found that generally, the results obtained are similar to that seen in Tables 4 through 6.

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Correspondence to T. M. Tonmoy Islam.

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Islam, T.M.T. Estimating the Elasticity of Growth in the US Using the Generalized Means of Income. Soc Indic Res 129, 95–112 (2016). https://doi.org/10.1007/s11205-015-1093-4