Misspecification

Misspecification refers to a situation in statistical modeling where the chosen model fails to reflect the true data-generating process. It can arise from incorrect assumptions about the functional form, the set of explanatory variables, the distribution of the error term, or how variables are measured.

Common forms include functional form misspecification, such as assuming linear relationships when they are nonlinear; omitted variable bias, where relevant predictors are left out; and distributional or error-structure misspecification, such as assuming homoskedastic, normal errors when this is not the case. Other sources include the inclusion of irrelevant variables, measurement error, endogeneity, and model misalignment with the underlying causal structure.

Misspecification can lead to biased and inconsistent estimates, incorrect standard errors, and unreliable confidence intervals, as well as poor predictive performance and misguided inferences.

Detection and assessment rely on specification tests and validation procedures. Examples include the Ramsey RESET test and other link tests for functional form, tests for heteroskedasticity and autocorrelation, and tests for endogeneity such as the Hausman test. Information criteria (AIC, BIC), residual diagnostics, cross-validation, and out-of-sample testing also help identify misspecification.

Mitigation options include revising the model specification, adding relevant variables, transforming or expanding the functional form, and adopting flexible approaches such as nonparametric or semi-parametric methods. Other remedies include instrumental variables to address endogeneity, robust standard errors, and model averaging to account for specification uncertainty.