BIC score in OLS

[Timea De Wispelaere]

Hello,

I have 4 different models which I estimated using OLS, in which more variables are added with each model. I determined the best model using the BIC. However, I have read that using BIC is more common in maximum likelihood estimations. On the contrary, I did not find a lot literature on BIC in OLS models. My question now is whether I can use BIC in the OLS context, and if not, why not? Should I better look at the adjusted R²?

For clarification, I include the output of one of my models:

. regress pctchangecarbonintensity firmsize profitability leverage age capitalintensity CAPEX K
> Zindex elektricitygenerator Carbonleakage i.Province_n SME  publicfirm

      Source |       SS           df       MS      Number of obs   =       158
-------------+----------------------------------   F(21, 136)      =      2.04
       Model |  3.44051682        21  .163834134   Prob > F        =    0.0078
    Residual |  10.8981796       136  .080133673   R-squared       =    0.2399
-------------+----------------------------------   Adj R-squared   =    0.1226
       Total |  14.3386964       157  .091329276   Root MSE        =    .28308

----------------------------------------------------------------------------------------------
    pctchangecarbonintensity |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
                    firmsize |  -.0471093   .0245416    -1.92   0.057    -.0956418    .0014233
               profitability |   1.063863   .8113558     1.31   0.192    -.5406424    2.668368
                    leverage |   .2303086   .1118611     2.06   0.041     .0090965    .4515208
                         age |  -.0023983   .0011083    -2.16   0.032    -.0045901   -.0002065
            capitalintensity |   .1056074   .1177671     0.90   0.371    -.1272841     .338499
                       CAPEX |   .3921912   .4245187     0.92   0.357    -.4473204    1.231703
                     KZindex |  -.0237426   .0197443    -1.20   0.231    -.0627881     .015303
        elektricitygenerator |   .2955618   .1491594     1.98   0.050     .0005901    .5905336
               Carbonleakage |   .0709142   .0514961     1.38   0.171    -.0309226     .172751
                             |
                  Province_n |
Brabant Wallon / Waals Br..  |   .1930119   .1302082     1.48   0.141    -.0644827    .4505065
                   Brussels  |    .096077   .0871738     1.10   0.272    -.0763145    .2684685
              East-Flanders  |  -.1108972   .0805239    -1.38   0.171    -.2701381    .0483437
       Hainaut / Henegouwen  |   .0719215    .086514     0.83   0.407    -.0991653    .2430083
         Limburg / Limbourg  |  -.0789072   .0860008    -0.92   0.360     -.248979    .0911645
               Liège / Luik  |   .0879246   .1032516     0.85   0.396    -.1162616    .2921109
                 Luxembourg  |  -.0083112   .1748158    -0.05   0.962      -.35402    .3373977
              Namur / Namen  |   .2386252   .2933795     0.81   0.417    -.3415505     .818801
Vlaams Brabant / Brabant ..  |  -.1705904   .1424057    -1.20   0.233    -.4522062    .1110255
              West-Flanders  |  -.0047872   .0961534    -0.05   0.960    -.1949364     .185362
                             |
                         SME |  -.2279518   .0749786    -3.04   0.003    -.3762267    -.079677
                  publicfirm |   .0392596   .1341881     0.29   0.770    -.2261056    .3046248
                       _cons |   .7746574   .4897592     1.58   0.116    -.1938711    1.743186
----------------------------------------------------------------------------------------------


. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |        Obs  ll(null)  ll(model)      df         AIC        BIC
-------------+---------------------------------------------------------------
           . |        158 -34.62127  -12.94635      22    69.89269   137.2698
-----------------------------------------------------------------------------
               Note: N=Obs used in calculating BIC; see [R] BIC note.

Thank you very much,

Timea

[Carlo Lazzaro]

Timea:
I would look at the adjusted R².

[Timea De Wispelaere]

Hello Carlo. Thank you for your answer! Could you also explain to me why? is it because BIC is designed for maximum likelihood?

[Carlo Lazzaro]

Timea:
because adj_Rsq is the usual criterion used for comparing linear regressssion models with different predictors but the same regressand.
See the valuable https://www.wiley.com/en-us/Introduc...-9780470032701, page 95; 113-114.

[Timea De Wispelaere]

thank you!

[Phil Bromiley]

To expand on Carlo's helpful comment, adjusted r-square, AIC and BIC for regression are really all dependent on the size of the squared errors. They impose different penalties for the number of parameters. While adjusted r-square is traditional in regression, I'm not sure that there is a strong theoretical argument for it being better than the others. Preferences among the may also vary by discipline as so many things do.