Macroeconomic Default Forecasts: Model Validity and Positive Rates
Summary
The document discusses a linear regression approach to forecasting corporate default rates from macroeconomic variables, using a historical dataset and scenario forecasts. The model selection goals are high adjusted R-squared and economic interpretability. The question raises whether including both GDP level and GDP growth creates multicollinearity, and notes that the fitted scenario forecasts produce negative default rates in some cases.
The response cautions that a strong fit statistic alone does not establish a meaningful economic model. It questions the identification and interpretation of the estimated relationships, pointing to coefficient signs that conflict with expected links between unemployment, GDP, and defaults. It suggests modeling the logarithm of the default rate to keep the implied rate positive. This is a brief conceptual suggestion rather than a worked model comparison; it does not diagnose the specific collinearity issue or address how to validate the forecast specification.
Key ideas
- A high adjusted R-squared does not by itself show that a default forecasting model is economically sound.
- Regression coefficients should be assessed for plausible economic interpretation.
- A model’s identification and theoretical basis matter when relating macroeconomic variables to defaults.
- Modeling the log of the default rate can constrain forecasts to positive values.
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Full text
# Forecasting default rates using a macroeconomic model # Forecasting default rates using a macroeconomic model 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: - that maximises the adjusted r-squared - that is economically intuitive 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. ## Answer by phdstudent (score 1) https://quant.stackexchange.com/a/42513 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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