If there is no data on income, It wouldn't be possible to produce an estimate of the Gini coefficient for the income distribution . Researcher may look into Census and see whether there are indicators that he/she can combine to produce some sort of index.

The lack of data makes diificult to carry out any scientific work. However, there are other income distribution and inequality indicators you can explore in addition to the Gini coefficient. The Palma ratio, the 20 / 20 ratio, the Theil index and the Hoover index.

If you have data on household expenses you can calculate a Gini or a 20/20 ratio using the distribution of expenses. It might be a good proxy for permanent income, even though might differ quite a bit from current income.

Proxy Ginis can also be calculated if decile distributions are available.