Christopher Dougherty EC220 - Introduction to econometrics (chapter 4) Slideshow: Ramsey’s reset...

Christopher Dougherty

EC220 - Introduction to econometrics (chapter 4)Slideshow: Ramsey’s reset test of functional misspecification

Original citation:

Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 4). [Teaching Resource]

© 2012 The Author

This version available at: http://learningresources.lse.ac.uk/130/

Available in LSE Learning Resources Online: May 2012

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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.

k

jjjXbbY

21

ˆ


2

Since, by definition, the fitted values are a linear combination of the explanatory variables, as shown, Y2 is a linear combination of the squares of the X variables and their interactions.

k

jjjXbbY

21

ˆ

^

Add to the regression specificationand test its coefficient


3

k

jjjXbbY

21

ˆ

2Y

If Y2 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.

^

Add to the regression specificationand test its coefficient


4

If the t statistic for the coefficient of is significant, this indicates that some kind of nonlinearity may be present.

k

jjjXbbY

21

ˆ

2Y


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.

. 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

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.

. reg EARNINGS S FITTEDSQ


------------------------------------------------------------------------------ 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

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.





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.




Copyright Christopher Dougherty 2011.

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/.

Individuals studying econometrics on their own and 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

or the University of London International Programmes distance learning course

20 Elements of Econometrics

www.londoninternational.ac.uk/lse.

11.07.25

Christopher Dougherty EC220 - Introduction to econometrics (chapter 4) Slideshow: Ramsey’s reset...

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