I am not sure if it is possible to draw up a poverty indicator only for the village level. Poverty indicators are constructed under the logic/quantitative and the objective is to compare and generalize the results from each country. This aproach creates a problem and the indicator does not take into account the particularities of each geographical context that generates poverty or inequality. Nowadays, the GINI coefficient is often used to measure this indicator.

As wikipedia said, the Gini coefficient (sometimes expressed as a Gini ratio or a normalized Gini index) (/d?ini/ jee-nee) is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measure of inequality. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability.

More information at https://en.wikipedia.org/wiki/Gini_coefficient

What I think we could do is adapt the ideas of Gini coefficient to the village level but I think it is very complicated to define an indicator per se only for a geographical level because there is a lot of economic, political and cultural heterogeneity.

Doesn't it similar to Human Development Index? We can develop a poverty index for a village with multidimensional poverty indicators. I have some experience of developing vulnerability index for villages based on household data, we can apply similar process to develop poverty index.

I would recommend making a livelihood analysis, which is more complex than trying to measure poverty, but which can reveal the complexity more completed. There are five livelihood capitals: natural, physical, human, financial and social. Livelihood capitals mean that they support people in securing their livelihoods. This means access and quality of these capitals are crucial as well as what leads to changes in access and quality. There is enormously much literature on these capitals. I suggest to get familiar with the approach and then formulate for each of the capitals two indicators you can measure. You might want to reflect, if it makes sense to include "legal capital". I feel that the existence of legal procedures, laws, etc can be seen as an assts as they often help people to get support when livelihoods are endangered. Please let me know in case you need some references, will send you some then.

as someone above mentioned i would recommend to use the same items as used by the "human development index" so that you create a data set that can be internationally compared and uses the same language and baseline as the UNDP data base does. http://hdr.undp.org/en/2016-report

Multidimensional poverty uses three dimensions (education, health and living conditions) and 10 indicators. The main problem of getting MPI is weighting and cutoffs. There is no scientific basis for weights and cutoff points that are needed in computing MPI, and MPI is sensitive to these parameters. The conventional poverty measure uses basic need approach where people can't meet their basic needs are considered as poor. Byt the way, this approach also uses multiple distentions (expenses made on food, education, non-food items and housing, etc) but translates all dimensions in monetary measure. There is a huge debate among economists whether MPI is a better measure of poverty. What we can say is that there is very high correlation between MPI and conventional poverty measure, meaning if we measure poverty using conventional measure, we are not missing out much. If a person can't meet his/her basic needs, then we expect that the person can't have good education, or better heath or healthy living condition. Indicators that are used in MPI are highly correlated with consumption expenditure or income of households. Of course, one can easily compute MPI for a village if you have required indicators.

https://doi.org/10.1080/1331677X.2021.1989319

See this article, it might be helpful

This is very true. Health, Nutrition, Access to Education, all of these matter.