# Regression on default rates and backward extrapolation

Suppose that we have bankruptcy data representative for Small and Medium-sized enterprises in a country. We can therefore calculate default rates. Furthermore suppose that we found that GDP, unemployment rates and interest rates seem to be significant macro economic factors that could explain there default rates.

Now we use regression to fit the macro economic variables to the observed default rates. My question now follows: If I suppose to have a portfolio of SME companies with only default rates from the last year. How could I using the above backward extrapolate these default rates, using the macro economic factors?

Thanks for any help!

• Please confirm: 1) You have firm level default (0/1) data in year $t$ 2) You have aggregate default rates (x percent) and macroeconomic controls for multiple years 3) You want to make firm specific predictions about default in other periods. Also, what does it mean to talk about default rates of firms that continue to exist in the present? Isn't the default rate among firms surviving into the present 0? Doesn't a firm become a new firm after default? – BKay Jan 15 '16 at 14:28
• Well I see it this way: I suppose to have a portfolio of a certain amount of companies (say only agricultural) and I only know the observed default rates of the past year/months. Yet I need more historical data to make a decent probability of default calibration. I want to use aggregate rates (say for SME) and assume it is representative for these agricultural companies. I then want to extrapolate (backwards), using underlying macro economic conditions, (I only assume to have those!) artificial default rates. One could see it as a stress test yet backwards, and the scenario is known. – user6717 Jan 15 '16 at 14:58