[Guest]

Dear Carlo,

Here is my result without detrending:

. reg log1 abs_r_mt rmt2

      Source |       SS           df       MS      Number of obs   =     2,418
-------------+----------------------------------   F(2, 2415)      =    200.50
       Model |  73.7438233         2  36.8719117   Prob > F        =    0.0000
    Residual |  444.111582     2,415  .183897135   R-squared       =    0.1424
-------------+----------------------------------   Adj R-squared   =    0.1417
       Total |  517.855405     2,417  .214255443   Root MSE        =    .42883

------------------------------------------------------------------------------
        log1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .2437952   .0158073    15.42   0.000     .2127979    .2747925
        rmt2 |  -.0220551   .0027192    -8.11   0.000    -.0273873   -.0167229
       _cons |   .1940486   .0152521    12.72   0.000       .16414    .2239573
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of log1
       Ho:  model has no omitted variables
                F(3, 2412) =      5.06
                  Prob > F =      0.0017

. estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of log1

         chi2(1)      =     2.13
         Prob > chi2  =   0.1441

After detrending:

. gen year=year(date)

. reg log1 abs_r_mt rmt2 i.year

      Source |       SS           df       MS      Number of obs   =     2,418
-------------+----------------------------------   F(11, 2406)     =    190.18
       Model |  240.853716        11  21.8957924   Prob > F        =    0.0000
    Residual |  277.001688     2,406  .115129546   R-squared       =    0.4651
-------------+----------------------------------   Adj R-squared   =    0.4627
       Total |  517.855405     2,417  .214255443   Root MSE        =    .33931

------------------------------------------------------------------------------
        log1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .1538489   .0128074    12.01   0.000     .1287342    .1789636
        rmt2 |  -.0159789   .0021665    -7.38   0.000    -.0202274   -.0117305
             |
        year |
       2002  |  -.2130969   .0310801    -6.86   0.000    -.2740435   -.1521503
       2003  |  -.0671241   .0309481    -2.17   0.030    -.1278118   -.0064363
       2004  |   .0917492   .0309159     2.97   0.003     .0311246    .1523739
       2005  |   .2934731   .0309407     9.49   0.000        .2328    .3541463
       2006  |   .3938697     .03096    12.72   0.000     .3331586    .4545808
       2007  |     .67599   .0313941    21.53   0.000     .6144277    .7375523
       2008  |   .6037664   .0316981    19.05   0.000      .541608    .6659249
       2009  |   .3832097    .031109    12.32   0.000     .3222066    .4442129
       2010  |   .2179331   .0309532     7.04   0.000     .1572354    .2786308
             |
       _cons |   .0458146   .0234033     1.96   0.050    -.0000781    .0917073
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of log1
       Ho:  model has no omitted variables
                F(3, 2403) =      3.18
                  Prob > F =      0.0230

. estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of log1

         chi2(1)      =     3.40
         Prob > chi2  =   0.0652

.

Out of curiosity, I also ran the regression with robust SE,

.  reg log1 abs_r_mt rmt2 i.year, robust

Linear regression                               Number of obs     =      2,418
                                                F(11, 2406)       =     186.33
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4651
                                                Root MSE          =     .33931

------------------------------------------------------------------------------
             |               Robust
        log1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .1538489   .0151115    10.18   0.000      .124216    .1834818
        rmt2 |  -.0159789   .0030179    -5.29   0.000    -.0218968   -.0100611
             |
        year |
       2002  |  -.2130969   .0325236    -6.55   0.000     -.276874   -.1493198
       2003  |  -.0671241   .0322656    -2.08   0.038    -.1303952   -.0038529
       2004  |   .0917492   .0288353     3.18   0.001     .0352047    .1482937
       2005  |   .2934731   .0324003     9.06   0.000     .2299377    .3570086
       2006  |   .3938697   .0302312    13.03   0.000     .3345879    .4531515
       2007  |     .67599   .0304858    22.17   0.000     .6162088    .7357712
       2008  |   .6037664   .0305015    19.79   0.000     .5439545    .6635784
       2009  |   .3832097   .0299544    12.79   0.000     .3244707    .4419487
       2010  |   .2179331   .0302593     7.20   0.000     .1585962      .27727
             |
       _cons |   .0458146   .0234242     1.96   0.051     -.000119    .0917482
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of log1
       Ho:  model has no omitted variables
                F(3, 2403) =      3.18
                  Prob > F =      0.0230

Do note that the coefficient of rmt2 is my estimate of interest, and I noticed that the t-stat of it keeps getting smaller, from -8 to -7 to -5 eventually, might it be a problem?

[Carlo Lazzaro]

Guest:
log-linear model seems to solve heteroskedasticity, but the main issue with your data is that you still have specification problem (as per RESET output).
You may try to plug in both the linear and the squared terms for -rmt- via -fvvarlist- notation.
Nothing relevant is happening with -rmt2- coefficient: no need to worry about that.

[Guest]

Dear Carlo,

-fvvarlist- notations were used in my initial regression, I was trying to make it more understandable by using more approachable notations (or so I thought I was), so sorry for confusing you. I will replicate my result using my original notations.

. gen log1 = log(csad)
(192 missing values generated)

. gen year=year(date)

. regress csad c.abs_r_mt##c.abs_r_mt

      Source |       SS           df       MS      Number of obs   =     2,609
-------------+----------------------------------   F(2, 2606)      =    369.70
       Model |  491.324057         2  245.662028   Prob > F        =    0.0000
    Residual |  1731.65225     2,606  .664486665   R-squared       =    0.2210
-------------+----------------------------------   Adj R-squared   =    0.2204
       Total |  2222.97631     2,608  .852368215   Root MSE        =    .81516

------------------------------------------------------------------------------
        csad |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .6120725    .028192    21.71   0.000     .5567915    .6673534
             |
  c.abs_r_mt#|
  c.abs_r_mt |  -.0587181   .0049878   -11.77   0.000    -.0684984   -.0489377
             |
       _cons |   1.051306   .0260192    40.41   0.000     1.000286    1.102327
------------------------------------------------------------------------------

. regress log1 c.abs_r_mt##c.abs_r_mt

      Source |       SS           df       MS      Number of obs   =     2,418
-------------+----------------------------------   F(2, 2415)      =    200.50
       Model |  73.7438233         2  36.8719116   Prob > F        =    0.0000
    Residual |  444.111582     2,415  .183897135   R-squared       =    0.1424
-------------+----------------------------------   Adj R-squared   =    0.1417
       Total |  517.855405     2,417  .214255443   Root MSE        =    .42883

------------------------------------------------------------------------------
        log1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .2437952   .0158073    15.42   0.000     .2127979    .2747925
             |
  c.abs_r_mt#|
  c.abs_r_mt |  -.0220551   .0027192    -8.11   0.000    -.0273873   -.0167229
             |
       _cons |   .1940486   .0152521    12.72   0.000       .16414    .2239573
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of log1
       Ho:  model has no omitted variables
                F(3, 2412) =      5.06
                  Prob > F =      0.0017

. estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of log1

         chi2(1)      =     2.13
         Prob > chi2  =   0.1441

.

I have also noticed that, after I logged my DV, both the R^2 and adjusted R^2 of my regression fell, should it not be of concern to me?

[Carlo Lazzaro]

Guest:
squared term makes sense in your regression.
However, the main issue now is to collect more predictors (as RESET outcome is significant).
The R^2 will probably increase as a result of plugging in more predictors (see the literature in your research field to get what Others did in the past when presented with the same research goal).

[Guest]

Dear Carlo,

My R^2 is actually consistent with the other researchers, and since I am using a time-series data, autocorrelation is found:

. gen year=year(date)

. regress csad c.abs_r_mt##c.abs_r_mt i.year

      Source |       SS           df       MS      Number of obs   =     2,609
-------------+----------------------------------   F(11, 2597)     =    253.85
       Model |  731.315933        11  66.4832667   Prob > F        =    0.0000
    Residual |  680.141573     2,597  .261895099   R-squared       =    0.5181
-------------+----------------------------------   Adj R-squared   =    0.5161
       Total |  1411.45751     2,608  .541203032   Root MSE        =    .51176

---------------------------------------------------------------------------------------
                 csad |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
             abs_r_mt |   .5762418   .0153312    37.59   0.000     .5461793    .6063044
                      |
c.abs_r_mt#c.abs_r_mt |  -.0557956   .0020825   -26.79   0.000    -.0598792    -.051712
                      |
                 year |
                2002  |  -.0984432   .0451764    -2.18   0.029    -.1870286   -.0098579
                2003  |    .122118   .0454211     2.69   0.007     .0330527    .2111833
                2004  |    .405986   .0452459     8.97   0.000     .3172644    .4947076
                2005  |   .7788927   .0451712    17.24   0.000     .6903174     .867468
                2006  |   .7770878   .0451397    17.22   0.000     .6885743    .8656013
                2007  |   .5912376   .0448429    13.18   0.000     .5033062    .6791691
                2008  |   .3693285   .0448179     8.24   0.000     .2814461     .457211
                2009  |   .2269734   .0450284     5.04   0.000     .1386782    .3152686
                2010  |   .1245081   .0452183     2.75   0.006     .0358406    .2131757
                      |
                _cons |   .4941324    .035398    13.96   0.000     .4247213    .5635435
---------------------------------------------------------------------------------------

. estat bgodfrey

Number of gaps in sample:  521

Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
    lags(p)  |          chi2               df                 Prob > chi2
-------------+-------------------------------------------------------------
       1     |        357.984               1                   0.0000
---------------------------------------------------------------------------
                        H0: no serial correlation

How do I, then, implement Newey-West Standard Errors in my regression to counter the effect of heteroskedasticity and autocorrelation? I will justify the use of the said Standard Error in the later part of my research and will try to fit an AR model but I will be happy for now as long as my regression can be interpreted normally, hence the use of Newey-West SE as a 'fast track'.

[Guest]

Dear Carlo,

I have figured out how to implement Newey-West SE in my regression, however, the following popped up:

. newey csad c.abs_r_mt##c.abs_r_mt, lag(0)

Regression with Newey-West standard errors      Number of obs     =      2,609
maximum lag: 0                                  F(  2,      2606) =     575.92
                                                Prob > F          =     0.0000

---------------------------------------------------------------------------------------
                      |             Newey-West
                 csad |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
             abs_r_mt |   .5900881   .0185185    31.86   0.000     .5537757    .6264006
                      |
c.abs_r_mt#c.abs_r_mt |  -.0573132    .002388   -24.00   0.000    -.0619958   -.0526307
                      |
                _cons |   .8116755   .0187512    43.29   0.000     .7749067    .8484443
---------------------------------------------------------------------------------------

. regress csad c.abs_r_mt##c.abs_r_mt

      Source |       SS           df       MS      Number of obs   =     2,609
-------------+----------------------------------   F(2, 2606)      =    728.54
       Model |  506.167349         2  253.083674   Prob > F        =    0.0000
    Residual |  905.290158     2,606   .34738686   R-squared       =    0.3586
-------------+----------------------------------   Adj R-squared   =    0.3581
       Total |  1411.45751     2,608  .541203032   Root MSE        =     .5894

---------------------------------------------------------------------------------------
                 csad |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
             abs_r_mt |   .5900881    .017454    33.81   0.000     .5558629    .6243133
                      |
c.abs_r_mt#c.abs_r_mt |  -.0573132   .0023925   -23.96   0.000    -.0620046   -.0526219
                      |
                _cons |   .8116755   .0185891    43.66   0.000     .7752247    .8481264
---------------------------------------------------------------------------------------

. newey csad c.abs_r_mt##c.abs_r_mt, lag(2)
date is not regularly spaced
r(198);

. newey csad c.abs_r_mt##c.abs_r_mt, lag(1)
date is not regularly spaced
r(198);

As I have mentioned before, I am dealing with stock market data and there will be days, for example, public holidays and the typical weekends, when the stock markets are not open. I then executed -force- to let Stata know that the missing dates were innocuous (I am not sure if this practice is okay), and the following showed up:

. newey csad c.abs_r_mt##c.abs_r_mt, lag(1) force

Regression with Newey-West standard errors      Number of obs     =      2,609
maximum lag: 1                                  F(  2,      2606) =     472.98
                                                Prob > F          =     0.0000

------------------------------------------------------------------------------
             |             Newey-West
        csad |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    abs_r_mt |   .5900881    .020285    29.09   0.000     .5503118    .6298645
             |
  c.abs_r_mt#|
  c.abs_r_mt |  -.0573132   .0025501   -22.48   0.000    -.0623136   -.0523128
             |
       _cons |   .8116755   .0217257    37.36   0.000     .7690742    .8542769
------------------------------------------------------------------------------

I am satisfactory with the outcome, as it has not changed significantly and my parameter of interest, the second row, gives me the same inference. Should I be glad that this is the case?

[Carlo Lazzaro]

Guest:
I'd be quite satisfied with those results, but the need for other predictors still holds.