A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Specification tests formally check whether key assumptions hold. The RESET test detects omitted nonlinearities by adding powers of fitted values; Hausman tests compare two estimators to detect endogeneity or misspecification.
Your work on hypothesis testing in regression gave you the tools to test whether individual coefficients are zero. Specification tests take that logic up a level: instead of testing a coefficient, you test whether the model itself is correctly formulated. The two most important tools — the Ramsey RESET test and the Hausman test — each target a different type of misspecification.
The RESET test (Regression Equation Specification Error Test) addresses functional form misspecification. Your prerequisites covered omitted variable bias: if a variable belongs in the model but isn't included, OLS estimates are biased. Ramsey's insight was that you don't need to know what the omitted variable is — if the functional form is wrong, the fitted values ŷ will contain information about the missing structure. The procedure: run your original regression, save the fitted values, then add ŷ², ŷ³ (and optionally ŷ⁴) to the model and test their joint significance with an F-test. If those powers are significant, the original model is misspecified — something nonlinear belongs in the regression. The RESET test is a general-purpose alarm: it tells you something is wrong, but not what to add. It's useful as a quick check before reporting results.
The Hausman test operates on a different principle: comparing two estimators that both converge to the same value under the null hypothesis but differ under the alternative. The most common application is testing for endogeneity. OLS is efficient under exogeneity; instrumental variables (IV) is consistent even under endogeneity but less efficient. Under the null that OLS is consistent, the OLS and IV estimates should be close. If they differ systematically — which the Hausman statistic formalizes — that's evidence that OLS is inconsistent due to endogeneity, and IV should be preferred. The test statistic is (β̂_IV - β̂_OLS)'[Var(β̂_IV) - Var(β̂_OLS)]⁻¹(β̂_IV - β̂_OLS), which is chi-squared distributed under the null.
The broader lesson is that regression results should be reported alongside a suite of diagnostics, not just coefficients and standard errors. A model that passes the RESET test provides more credibility that the functional form is correct. A model where OLS and a valid IV give similar results provides evidence against endogeneity. Neither test is foolproof — the RESET test can miss certain misspecifications, and the Hausman test requires a valid instrument — but together they constitute a minimum standard for responsible empirical work.