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Specification & Data Problemsintermediate

Functional Form Misspecification and RESET

Functional form misspecification occurs when the chosen equation omits nonlinearity, such as a missing square, interaction, or log, so the conditional mean is wrong. Ramsey’s RESET test adds powers of the fitted values, usually y^2\hat{y}^2 and y^3\hat{y}^3, to the model and tests their joint significance with an FF test. A significant statistic signals that some nonlinear function of the regressors belongs in the model. Getting the form wrong biases coefficients and predictions, even when every classical assumption about the error otherwise holds.

Why it matters

RESET is a clever trick. The fitted values are built from your regressors, so their squares and cubes stand in for nonlinear terms you might have left out. If those powers add explanatory power, your straight-line specification is missing curvature somewhere. The test does not tell you which variable needs a square or a log, only that the current shape is too simple. It is a smoke alarm for functional form, not a blueprint for the fix.

Formulas

RESET auxiliary regression
y=β0+βx+δ1y^2+δ2y^3+errory=\beta_0+\boldsymbol{\beta}\mathbf{x}+\delta_1 \hat{y}^{2}+\delta_2 \hat{y}^{3}+\text{error}
y^\hat{y} comes from the original OLS fit. Test H0:δ1=δ2=0H_0:\delta_1=\delta_2=0; rejection points to functional form misspecification.
RESET F statistic
F=(Rnew2−Rold2)/q(1−Rnew2)/(n−k−1−q)F=\frac{(R_{\text{new}}^2-R_{\text{old}}^2)/q}{(1-R_{\text{new}}^2)/(n-k-1-q)}
qq is the number of added powers (usually q=2q=2). Under H0H_0, F∼Fq, n−k−1−qF\sim F_{q,\,n-k-1-q} approximately.

Worked examples

Scenario

Check whether a level-level housing price model misses nonlinearity.

Solution

After `regress price lotsize sqrft bdrms`, run `estat ovtest`, Stata’s implementation of Ramsey RESET. A small pp-value rejects correct specification, suggesting that logs or squared terms (for example `c.sqrft##c.sqrft`) should enter. Re-estimating with logs often clears the test.

NotePlain `estat ovtest` uses powers of the fitted values (that is RESET), while `estat ovtest, rhs` uses powers of the regressors instead. Stata adds powers up to y^4\hat{y}^4, so its degrees of freedom are 3, not 2.
Scenario

Compare a linear wage model against a log specification using RESET.

Solution

Run `regress wage educ exper` then `estat ovtest`; if it rejects, try `regress lwage educ c.exper##c.exper` and re-run the test. A specification that passes RESET while keeping coefficients interpretable is preferred, illustrating that RESET guides the search for a better form without dictating the exact terms.

Common mistakes

  • ✗Reading a RESET rejection as proof of which variable needs transforming. It only flags that some nonlinearity is missing, not where.
  • ✗Thinking RESET detects omitted variables in general. It targets functional form; a truly omitted regressor that is uncorrelated with the included ones may pass undetected.
  • ✗Believing a passed RESET guarantees the model is correct. It is a specification check with limited power, not a certificate of truth.
  • ✗Confusing RESET with a heteroskedasticity test. RESET concerns the mean function, while tests like Breusch-Pagan concern the error variance.

Revision bullets

  • •Wrong functional form biases coefficients and predictions.
  • •RESET adds y^2,y^3\hat{y}^2,\hat{y}^3 and jointly tests them with an FF test.
  • •Rejection means some nonlinearity is missing, not which term.
  • •In Stata, `estat ovtest` runs Ramsey RESET after `regress`.
  • •RESET checks the mean function, not the error variance.

Quick check

Ramsey’s RESET test works by:

A significant RESET statistic tells you that:

Connected topics

Omitted var biasMLR assumptionsF testLogs & Elastic.Poly & Inter.

Sources

  1. Wooldridge (2019), §9.1
    Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 7th ed. Cengage, 2019.
    Presents functional form misspecification and the Ramsey RESET test using powers of the fitted values.
  2. Wooldridge (2019), §9.1b
    Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 7th ed. Cengage, 2019.
    Discusses the consequences of misspecified functional form for coefficient interpretation and prediction.
How to cite this page
Dr. Phil's Quant Lab. (2026). Functional Form Misspecification and RESET. Derivatives Atlas. https://phucnguyenvan.com/concept/efm-reset-misspecification
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