It's meaningless to talk about poverty rate without talking about the poverty line.
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Free and open access to global development data
data.worldbank.org
Switzerland's poverty rate is >3x of Vietnam's, but that doesn't mean Switzerland is poorer than Vietnam.
Developed countries usually adopt the concept of relative poverty, while developing countries usually adopt the concept of absolute poverty.
In many developed countries, the poverty line is defined as a percentage (eg; 60%) of the median income. Which means, the higher the median income, the higher the poverty line. As such, there will ALWAYS be a percentage of population under the poverty line based on income distribution (unless you are a communist country with everyone making the same level of income). You can never grow out of poverty because the goalpost shifts every year as you grow.
US poverty line:
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Meanwhile in many developing countries, the poverty line is usually defined as the minimum resources required to secure basic living necessities. Eg; in China the poverty line is fixed at RMB4000 per year. The line is fixed, and it's possible to grow out of poverty.
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As you can see, the poverty line can be very different between countries. A family of four in the US which makes less than USD30K pa is considered under the poverty line. That's USD2.5k or around RMB17.5K per month.
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No cities in mainland China have their median household income above USD30K pa, not even the first-tier cities.
We can adjust for price differences with PPP ratio; China's PPP to nominal ratio is around 0.6.
USD30K in the US is worth ~USD18K in China. Then yeah, some cities like Beijing or Shanghai have median household income above the poverty rate in the US. However these cities are more expensive than the national average, so the PPP ratio should be higher and lesser adjustment is needed, but whatever.