Ramsey RESET test confusion

[Cam Fenlon]

As I understand, the Ramsey RESET test (although called ovtest on Stata), is not actually a general test for omitted variable bias. Rather, it is a test for misspecification. Specifically, if the model is properly specified, "no nonlinear functions of the independent variables should be significant when added to the estimated equation". So now I'm confused because after estimating three models, I get the following:

Log-log model with two independent variables:

Translog model with five independent variables:

Augmented log-log model with a dummy variable:

So according to this, the null of no omitted variables (or no misspecification) will be rejected for the first two but not the last (at 5% sig. level). Yet, the translog is essentially the log-log with higher powers of the independent variable, so I'm confused as to what to conclude from this. I'm inclined to say that the dummy variable was an important omitted variable, but then again RESET is not a general test for OVB.

Any help is appreciated.

[Carlo Lazzaro]

Cam:
try -linktest-.
That said, I would also take a look at Adj-Rsq to have a more comprehensive idea about your regression models.

[Joao Santos Silva]

Dear Cam Fenlon,

Let me try to add something to this thread.

First, note that as far as I understand, Stata performs this test without using robust standard errors. That means that the test is only valid under restrictive conditions. Second, doing the test with 3 powers is likely to lead to a test with reasonably low power; doing the test just with squares or squares and cubes is likely to be better. For these reasons, I suggest that you run the test "manually".

Second, note that is perfectly possible that a model with fewer regressors passes the test and a model with added regressors fails.

Finally, indeed you cannot conclude anything about the significance of the dummy from the result of the test.

Best wishes,

Joao

[Ramiro Flores]

Dear Prof @Joao Santos Silva

I am running linear regression and the test for heteroskedasticity tells me that there is heteroscedasticity in my linear regression model
Considering the heteroskedasticity I am manually running a Ramsey test as follows:

  regress Y X1 X1_2 X3 X4 X5 X1_X5

      Source |       SS           df       MS      Number of obs   =       305
-------------+----------------------------------   F(6, 298)       =     16.81
       Model |  235.054666         6  39.1757776   Prob > F        =    0.0000
    Residual |  988.528251       298   3.3172089   R-squared       =    0.4921
-------------+----------------------------------   Adj R-squared   =    0.2758
       Total |  1223.58292       304  4.02494381   Root MSE        =    1.8213

------------------------------------------------------------------------------
   Y    | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     X1 |  -23.93932   19.00714    -1.92   0.001    -113.1506    1.271934
   X1_2 |   15.09599   19.89408     1.51   0.131    -9.054695    69.24668
     X3 |  -.1880227   .0807115    -1.59   0.214    -.2868593     .030814
     X4 |   .0198651   .0002227     3.44   0.013     .0003269    .0012034
     X5 |  -.3142902   .0006033    -2.14   0.054    -.0024775   -.0001029
  X1_X5 |   .1224941   .0007317     2.04   0.032     .0000541     .002934
  _cons |    7.32069   10.66907     2.56   0.001     6.324433    48.31695
------------------------------------------------------------------------------

estat hettest, fstat

Breusch–Pagan/Cook–Weisberg test for heteroskedasticity 
Assumption: i.i.d. error terms
Variable: Fitted values of Y

H0: Constant variance

F(1, 303) =   8.62
 Prob > F = 0.0019

predict double yhat
(option xb assumed; fitted values)

gen double yhat2 = yhat ^2

regress Y X1 X1_2 X3 X4 X5 X1_X5 yhat2, vce(robust)

Linear regression                               Number of obs     =        305
                                                F(7, 297)         =      18.23
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2537
                                                Root MSE          =     2.8225

------------------------------------------------------------------------------
        |               Robust
   Y    | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     X1 |  -117.0714   71.95451    -1.63   0.105    -258.6767    24.53385
   X1_2 |   67.47439   44.74207     1.51   0.133    -20.57728    155.5261
     X3 |  -.1571065   .0705368    -2.23   0.027    -.2959217   -.0182912
     X4 |   .0011074   .0004372     2.53   0.012     .0002471    .0019677
     X5 |  -.0014616   .0004976    -2.94   0.004    -.0024408   -.0004823
  X1_X5 |   .0016805   .0006054     2.78   0.006     .0004891    .0028719
  yhat2 |  -.0965039   .1034855    -0.93   0.352    -.3001617    .1071539
  _cons |   52.45714    29.1021     1.80   0.072    -4.815313    109.7296
------------------------------------------------------------------------------

. test yhat2

 ( 1)  yhat2 = 0

       F(  1,   297) =    0.87
            Prob > F =    0.3518

I am right? or
How can I manually run the Ramsey test considering heteroskedasticity?
Thanks and regards, Ramiro Flores

[Joao Santos Silva]

This looks fine to me.

Best wishes,

Joao

[Ramiro Flores]

Thanks dear Prof @Joao Santos Silva