19 Ramseys RESET Test: REgression Specification Error Test
Consider the model (1) General test for misspecification of
functional form If LSA #1 holds, then no non-linear function of the
Xs should be significant when added to the model. Consider (2) Null
hypothesis is that (1) is correctly specified How many powers of
predicted values to include? Conduct F-test on powers of predicted
values J.B. Ramsey (1969), Tests for Specification Error in
Classical Linear Least Squares Regression Analysis. Journal of the
Royal Statistical Society, Series B 31, 350371
Slide 20
20 Ramseys RESET Test. reg test str avginc, r Linear regression
Number of obs = 420 F( 2, 417) = 132.65 Prob > F = 0.0000
R-squared = 0.5115 Root MSE = 13.349
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| Robust testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
str | -.6487401.3533403 -1.84 0.067 -1.34329.04581 avginc |
1.839112.114733 16.03 0.000 1.613585 2.064639 _cons | 638.7292
7.301234 87.48 0.000 624.3773 653.081
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estat ovtest (can just type. ovtest) Ramsey RESET test using powers
of the fitted values of testscr Ho: model has no omitted variables
F(3, 414) = 18.36 Prob > F = 0.0000
Slide 21
21 Ramseys RESET Test. reg test str avginc avginc2, r Linear
regression Number of obs = 420 F( 3, 416) = 286.55 Prob > F =
0.0000 R-squared = 0.5638 Root MSE = 12.629
------------------------------------------------------------------------------
| Robust testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
str | -.9099512.3545374 -2.57 0.011 -1.606859 -.2130432 avginc |
3.881859.2709564 14.33 0.000 3.349245 4.414474 avginc2 |
-.044157.0049606 -8.90 0.000 -.053908 -.034406 _cons | 625.2308
7.087793 88.21 0.000 611.2984 639.1631
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estat ovtest Ramsey RESET test using powers of the fitted values of
testscr Ho: model has no omitted variables F(3, 413) = 2.48 Prob
> F = 0.0605
Slide 22
22 Ramseys RESET Test. reg test str avginc avginc2 avginc3, r
Linear regression Number of obs = 420 F( 4, 415) = 207.23 Prob >
F = 0.0000 R-squared = 0.5663 Root MSE = 12.608
------------------------------------------------------------------------------
| Robust testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
str | -.9277523.3562919 -2.60 0.010 -1.628114 -.2273905 avginc |
5.124736.7045403 7.27 0.000 3.739824 6.509649 avginc2 |
-.1011073.0287052 -3.52 0.000 -.157533 -.0446815 avginc3
|.0007293.0003414 2.14 0.033.0000582.0014003 _cons | 617.8974
7.926373 77.95 0.000 602.3165 633.4782
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estat ovtest Ramsey RESET test using powers of the fitted values of
testscr Ho: model has no omitted variables F(3, 412) = 1.79 Prob
> F = 0.1490
Slide 23
23 Ramseys RESET Test. reg test str el_pct meal_pct, r Linear
regression Number of obs = 420 F( 3, 416) = 453.48 Prob > F =
0.0000 R-squared = 0.7745 Root MSE = 9.0801
------------------------------------------------------------------------------
| Robust testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
str | -.9983092.2700799 -3.70 0.000 -1.529201 -.4674178 el_pct |
-.1215733.0328317 -3.70 0.000 -.18611 -.0570366 meal_pct |
-.5473456.0241072 -22.70 0.000 -.5947328 -.4999583 _cons | 700.15
5.56845 125.74 0.000 689.2042 711.0958
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estat ovtest Ramsey RESET test using powers of the fitted values of
testscr Ho: model has no omitted variables F(3, 413) = 6.29 Prob
> F = 0.0004
Slide 24
24 Ramseys RESET Test. reg test str el_pct meal_pct avginc, r
Linear regression Number of obs = 420 F( 4, 415) = 467.42 Prob >
F = 0.0000 R-squared = 0.8053 Root MSE = 8.4477
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| Robust testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
str | -.5603892.2550641 -2.20 0.029 -1.061768 -.0590105 el_pct |
-.1943282.0332445 -5.85 0.000 -.2596768 -.1289795 meal_pct |
-.3963661.0302302 -13.11 0.000 -.4557895 -.3369427 avginc
|.674984.0837161 8.06 0.000.5104236.8395444 _cons | 675.6082
6.201865 108.94 0.000 663.4172 687.7992
------------------------------------------------------------------------------.
estat ovtest Ramsey RESET test using powers of the fitted values of
testscr Ho: model has no omitted variables F(3, 412) = 0.47 Prob
> F = 0.7014
Slide 25
25 Ramseys RESET Test: replicated. predict yh (option xb
assumed; fitted values). sum yh Variable | Obs Mean Std. Dev. Min
Max
-------------+--------------------------------------------------------
yh | 420 654.1565 17.09817 614.9183 702.8387. gen yhz =
(yh-r(mean))/r(sd). sum yh* Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
yh | 420 654.1565 17.09817 614.9183 702.8387 yhz | 420 1.22e-09 1
-2.294882 2.847214. gen yhz2=yhz*yhz. gen yhz3=yhz^3. gen
yhz4=yhz^4