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Explain how a wrongly specified model distorts regression output and how the usual specification errors can be prevented

CFA® Level II · Quantitative Methods · Model Misspecification · L2.QM.3.a

The idea

A model is misspecified when its form or its variables are wrong, and the damage can reach the coefficients themselves. Leaving out a relevant variable that is correlated with an included one biases the included coefficient and makes it inconsistent. An inappropriate functional form, such as a straight line where the relationship is logarithmic, leaves patterns in the residuals. Inappropriate scaling can create heteroskedasticity or multicollinearity. Inappropriate pooling mixes data from different regimes, and it often shows as separate clusters in a residual plot. The cure is sound economic reasoning before estimation, parsimony, checking the residuals, and testing the model out of sample. Remember that a high R² does not rule out misspecification.

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