1. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION 1 Ramsey’s RESET test of functional misspecification is intended to provide a simple indicator of evidence of nonlinearity. To implement it, one runs the regression and saves the fitted values of the dependent variable.

2. 2 Since, by definition, the fitted values are a linear combination of the explanatory variables, as shown, Y 2 is a linear combination of the squares of the X variables and their interactions. ^ RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION

3. 3 If Y 2 is added to the regression specification, it should pick up quadratic and interactive nonlinearity, if present, without necessarily being highly correlated with any of the X variables. ^ RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION Add to regression specification

4. 4 If the t statistic for the coefficient of is significant, this indicates that some kind of nonlinearity may be present. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION

5. 5 We will do this for a wage equation. Here is the output from a simple linear regression of EARNINGS on S using EAEF Data Set 21. We save the fitted values as FITTED and generate FITTEDSQ as the square. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION. reg EARNINGS S Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 112.15 Model | 19321.5589 1 19321.5589 Prob > F = 0.0000 Residual | 92688.6722 538 172.283777 R-squared = 0.1725 -------------+------------------------------ Adj R-squared = 0.1710 Total | 112010.231 539 207.811189 Root MSE = 13.126 ------------------------------------------------------------------------------ EARNINGS | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- S | 2.455321.2318512 10.59 0.000 1.999876 2.910765 _cons | -13.93347 3.219851 -4.33 0.000 -20.25849 -7.608444 ------------------------------------------------------------------------------. predict FITTED (option xb assumed; fitted values). gen FITTEDSQ = FITTED*FITTED

6. 6 The coefficient of FITTEDSQ is significant at the 5 percent level and nearly at the 1 percent level, indicating that the addition of the square of S would improve the specification of the model. We saw this in a previous slideshow. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION. reg EARNINGS S FITTEDSQ Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 59.69 Model | 20372.4957 2 10186.2479 Prob > F = 0.0000 Residual | 91637.7353 537 170.647552 R-squared = 0.1819 -------------+------------------------------ Adj R-squared = 0.1788 Total | 112010.231 539 207.811189 Root MSE = 13.063 ------------------------------------------------------------------------------ EARNINGS | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- S | -.6956444 1.290509 -0.54 0.590 -3.230709 1.83942 FITTEDSQ |.0303508.0122302 2.48 0.013.006326.0543757 _cons | 16.35854 12.62009 1.30 0.195 -8.432256 41.14933 ------------------------------------------------------------------------------

7. 7 However, we also saw that it was better still to use a semilogarithmic specification. The RESET test is intended to detect nonlinearity, but not be specific about the most appropriate nonlinear model. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION. reg EARNINGS S FITTEDSQ Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 59.69 Model | 20372.4957 2 10186.2479 Prob > F = 0.0000 Residual | 91637.7353 537 170.647552 R-squared = 0.1819 -------------+------------------------------ Adj R-squared = 0.1788 Total | 112010.231 539 207.811189 Root MSE = 13.063 ------------------------------------------------------------------------------ EARNINGS | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- S | -.6956444 1.290509 -0.54 0.590 -3.230709 1.83942 FITTEDSQ |.0303508.0122302 2.48 0.013.006326.0543757 _cons | 16.35854 12.62009 1.30 0.195 -8.432256 41.14933 ------------------------------------------------------------------------------

8. 8 It may fail to detect some types of nonlinearity. However it does have the virtues of being very easy to implement and consuming only one degree of freedom. RAMSEY’S RESET TEST OF FUNCTIONAL MISSPECIFICATION. reg EARNINGS S FITTEDSQ Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 2, 537) = 59.69 Model | 20372.4957 2 10186.2479 Prob > F = 0.0000 Residual | 91637.7353 537 170.647552 R-squared = 0.1819 -------------+------------------------------ Adj R-squared = 0.1788 Total | 112010.231 539 207.811189 Root MSE = 13.063 ------------------------------------------------------------------------------ EARNINGS | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- S | -.6956444 1.290509 -0.54 0.590 -3.230709 1.83942 FITTEDSQ |.0303508.0122302 2.48 0.013.006326.0543757 _cons | 16.35854 12.62009 1.30 0.195 -8.432256 41.14933 ------------------------------------------------------------------------------

9. Copyright Christopher Dougherty 2012. These slideshows may be downloaded by anyone, anywhere for personal use. Subject to respect for copyright and, where appropriate, attribution, they may be used as a resource for teaching an econometrics course. There is no need to refer to the author. The content of this slideshow comes from Section 4.3 of C. Dougherty, Introduction to Econometrics, fourth edition 2011, Oxford University Press. Additional (free) resources for both students and instructors may be downloaded from the OUP Online Resource Centre http://www.oup.com/uk/orc/bin/9780199567089/http://www.oup.com/uk/orc/bin/9780199567089/. Individuals studying econometrics on their own who feel that they might benefit from participation in a formal course should consider the London School of Economics summer school course EC212 Introduction to Econometrics http://www2.lse.ac.uk/study/summerSchools/summerSchool/Home.aspx http://www2.lse.ac.uk/study/summerSchools/summerSchool/Home.aspx or the University of London International Programmes distance learning course EC2020 Elements of Econometrics www.londoninternational.ac.uk/lsewww.londoninternational.ac.uk/lse. 2012.11.04