Misspecifikation

Misspecifikation refers to a mismatch between a chosen model and the real-world process it is intended to describe. In statistics, econometrics, and related fields, misspecification occurs when the model’s assumptions about structure, variables, relationships, or the distribution of errors do not hold for the data. This can lead to biased or inconsistent estimates, invalid inference, and unreliable predictions.

Common sources of misspecification include incorrect functional form (for example, assuming linear relationships when the true relationship is nonlinear), omitted variables (relevant predictors left out), and incorrect error assumptions (such as assuming normality or homoskedasticity when these do not apply). Endogeneity, measurement error in variables, and dynamic misspecification (ignoring lagged effects or time dependencies) are also frequent causes. Structural changes or regime shifts can produce misspecification over time.

The consequences of misspecification are substantial. Estimation may be biased or inconsistent, standard errors and test statistics can be invalid, and both forecasts and policy conclusions may be misleading. In causal analysis, misspecification can distort estimated treatment effects; in forecasting, it degrades predictive accuracy.

Detection and assessment rely on diagnostics and tests, including residual analysis and specification tests such as the Ramsey RESET test for nonlinearities, as well as information criteria (AIC, BIC) and cross-validation for model comparison. No test can guarantee correctness, but diagnostics help identify areas where models may be improved.

Remedies focus on model revision: adding relevant variables, transforming or interacting terms, or adopting flexible approaches (nonparametric methods, splines, generalized additive models). Other strategies include addressing endogeneity with instrumental variables, using robust or error-in-variables models, and model averaging or Bayesian model selection to mitigate the impact of misspecification.