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I am trying to forecast corporate default rates using macroeconomic data. I have a few explanatory variables (all the variables are explained in figure 2), which range from 2000 to 2017. On this dataset I computed my linear regression. Additionaly we were given three scenarios, which we had to forecast on. We were asked to come up with a model:

  1. that maximises the adjusted r-squared
  2. that is economically intuitive

Figure 1 Figure 2

After some iterations I was able to come up with a model that has an adjusted r-squared of 0.935. Having such a high adjusted r-squared I fear that I have ran into the trap of multicollinearity, as one variable would be the absolute GDP value and the other would be the GDP rate of change YoY. So my first question would be: Is this a case of multicollinearity or not? And if yes, which variable would be the best to regress on? The absolute GDP or the yearly change in the GDP?

Next, when forecasting the corporate default using the just computed linear regression I get negative default rates. This is obviously not economically intuitive and violates the second requirement. As can be seen from the plot below, the default rates are only positive for the pessimistic case. So my second question would be: Is it possible to force the response variable (corporate default rates) to stay positive.

Figure 3

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I guess more than multicolinearity you are running into the issue of identification. What are you exactly identifying with such a regression? You somehow need to instrument for defaults. Although your $R^2$ is high, does your regression make any sense?

Take for example the coefficient on unemployment. It is negative, so that seems to imply that higher unemployment leads to lower default rates. This is fairly weird. The same on the coefficients of GDP and GDP growth.

Basically, it is hard to economically explain defaults with such a reduced form regression with no theory behind it.

Finally, regarding your last point of defaults becoming negative, you can always take logs of the right hand side variable to ensure that it's exponent (the default rate) is always positive.

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  • $\begingroup$ Yes, some of the coefficients are fairly counter-intuitive. Same as you did I went ahead and discussed them and then ignored them going forth. If I am correct I should be aiming for a regression output which is economically more intuitive? Going forth I also tried a Logit regression which should be the same what you described and got negative default rates, which leads me to believe that I did it wrong. Thank you for your help! $\endgroup$ – Siroffinance Nov 5 '18 at 15:12

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