# How to compute the Wealth Lorenz curve with negative values?

I have some data with asset holdings (wealth) of a large group of people. I want to compute the Lorenz curve and Gini coefficient of my population. The problem is that a large fraction of people have negative wealth.

Say I have wealth that ranges from -1 to 4. About 50% of people have 0 or less wealth. The other remaining households have positive values. In this imaginary country, for every lender we have a borrower, so if we add all of the wealth of everybody we would get a total net wealth of zero. How can I compute the Lorenz curve?

My intuition, which I suspect is wrong, is to move the mass of people with negative wealth to zero. That is, the Lorenz curve only starts to move upwards from 0.5 on the x axis onward. Do you have any suggestions or example?

• The assumption that income or wealth is non-negative really is important for this graph. OTOH it's hard to believe that this complication is not discussed in the income inquality literature. – Nick Cox Sep 17 '16 at 14:21
• Where does your "wealth" data come from? Perhaps it was standardized? – GeoMatt22 Sep 17 '16 at 14:46
• @GeoMatt22 From a macroeconomic, general equilibrium model (theoretical values). I do have wealth data from the US where a large fraction of households have negative values and I need to compare the results to those of my theoretical model. None of the data is standardized. – Sophie Sep 17 '16 at 14:50
• "if we add all of the wealth of everybody we would get a total net wealth of zero" seems wrong if the data are not standardized. There can be some debtors and some debt holders, but the economy as a whole should certainly have positive assets? I do not do economics, but even Wikipedia says "Normally the mean (or total) is assumed positive, which rules out a Gini coefficient less than zero." – GeoMatt22 Sep 17 '16 at 15:19
• @GeoMatt22 what you are saying is correct in the real world, where there are many different types of assets and some of the lending can happen between countries. In my theoretical model I have only one asset, private debt, and its a closed economy, so for every lender I need a borrower and netting out their asset positions should be zero, by definition. But even with real world data, how could I standardize wealth so that I can plot a Lorenz Curve? – Sophie Sep 17 '16 at 23:45