A regression can report a 0.88 R-squared, a wildly significant F-statistic, and still be useless. Broken assumptions do not break the fit; they break the standard errors, and the standard errors are what you use to make decisions.
Model specification is the set of variables you include plus the functional form of the equation. Five principles govern it. The model should rest on economic reasoning for each variable. It should be parsimonious, meaning every regressor earns its place. It should perform out of sample, not just on training data (a model that fails here is overfit). Its functional form should match the true relationship. And it should satisfy the regression assumptions.
- Omitted variables: an important regressor is left out. May induce heteroskedasticity or serial correlation.
- Inappropriate form of variables: a nonlinear relationship is fit as linear. Often cured by taking natural logs when the relation is proportional. May induce heteroskedasticity.
- Inappropriate scaling: raw data used where scaled data (common-size statements) is right. May induce heteroskedasticity or multicollinearity.
Common mistakes
- Treating unconditional heteroskedasticity as fatal. Only the conditional form, where error variance tracks the regressors, corrupts inference.
- Expecting robust corrections to change coefficients. They change only standard errors. A coefficient of 1.2414 stays 1.2414.
- Assuming inflated t-statistics under multicollinearity. Heteroskedasticity and serial correlation inflate t-statistics; multicollinearity deflates them by inflating standard errors.
Bottom line
- Specification principles: economic grounding, parsimony, out-of-sample performance, correct functional form, no assumption violations
- Form failures: omitted variables, wrong variable form, wrong scaling, inappropriate pooling
- Omitted variable correlated with a regressor makes coefficients and standard errors biased and inconsistent; uncorrelated biases only the intercept
- Conditional heteroskedasticity underestimates standard errors, inflates t-statistics, raises Type I errors; unconditional is harmless for inference
Exam shortcut
Read the symptom, name the violation. Significant F with insignificant t-statistics and a high R-squared is always multicollinearity; compute or read the VIF and check it against 5 and 10. Residual spread widening or narrowing with the x-variable is heteroskedasticity; the BP p-value below 0.05 seals it. Time-series data plus a mention of persistent residual signs is serial correlation; the BG test is your tool.
The full lesson (about 2,004 words, 13 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.
Learning objectives
- model misspecification
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