# Regression on default data 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?

• I think you may need to be much more precise about your analysis to get better advice. Using regression just is too broad a description: is this panel data, etc.? The bottom lines include (a) no model is guaranteed to perform well with quite different inputs (b) you may not have practical alternatives. – Nick Cox Jan 15 '16 at 12:58
• If you want details; I used a brute force regressions (univariate) to find macroeconomic factors that seem significant for certain default rate sets ($R^2$ big). One can use different kind of regression methods (say log transform) to regress default rates on GDP, unemployment rates, interest rates (significant factors) to find coefficients etc. But say we assume this default set is representative of a smaller portfolio (which only has few observations) could one using this knowledge to extrapolate to obtain more historical default rates? – user100783 Jan 15 '16 at 14:13