Missing R square in 2 SLS

[hussein bataineh]

Hi please im using ivregress to run 2 SLS , and it appear that R-squared is missing R-squared = . is this mean that i have problem in my data or the result is not sufficient and is there a way to solve it



asdoc ivregress 2sls hard_final_Exact_new Firm_Size_w ROA_four_w DCAPEX_w TAX_rate_w Leverage_w Market_book_four_w FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w Governance_Score_w Fund_Status_w FUNDING_RATIO_w Platn_Size_w Contribut_pension_three_w ACTUAL_RETURN_w PensionBenefitsDiscountRate_w CSR_Committee SustainabilityScore_w i.year i.ff_12 (csopresence1 = CSO_Percentage ) , first robust replace nest drop( i.year i.ff_12 ) dec(4) save(mss)


estat first, forcenonrobust
estat endogenous csopresence1

 Instrumental variables 2SLS regression            Number of obs   =      3,059
                                                  Wald chi2(45)   =      56.36
                                                  Prob > chi2     =     0.1193
                                                  R-squared       =          .
                                                  Root MSE        =     .15783

-----------------------------------------------------------------------------------------------
                              |               Robust
         hard_final_Exact_new | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
------------------------------+----------------------------------------------------------------
                 csopresence1 |   .1042133   .0459817     2.27   0.023     .0140909    .1943358
                  Firm_Size_w |   -.005251   .0053861    -0.97   0.330    -.0158076    .0053056
                   ROA_four_w |  -.4158489   .1277174    -3.26   0.001    -.6661705   -.1655273
                     DCAPEX_w |  -.0145154   .2138214    -0.07   0.946    -.4335977    .4045669
                   TAX_rate_w |  -.0029006   .0141369    -0.21   0.837    -.0306084    .0248073
                   Leverage_w |  -.0253021    .024828    -1.02   0.308     -.073964    .0233598
           Market_book_four_w |  -.0001865   .0006804    -0.27   0.784      -.00152     .001147
             FREE_CASH_FLOW_w |   .3186146   .1257625     2.53   0.011     .0721247    .5651046
       CASH_FLOW_VOLATILITY_w |  -.0503814   .1943168    -0.26   0.795    -.4312354    .3304725
           Governance_Score_w |   .0003144   .0001643     1.91   0.056    -7.66e-06    .0006364
                Fund_Status_w |  -.3227381   .1731365    -1.86   0.062    -.6620793    .0166032
              FUNDING_RATIO_w |  -.0278129    .022463    -1.24   0.216    -.0718395    .0162138
                 Platn_Size_w |  -.0078465   .0046602    -1.68   0.092    -.0169804    .0012874
    Contribut_pension_three_w |  -.2299897   .0739341    -3.11   0.002    -.3748979   -.0850816
              ACTUAL_RETURN_w |   .0529899   .0508561     1.04   0.297    -.0466862    .1526659
PensionBenefitsDiscountRate_w |    .014494   .0052503     2.76   0.006     .0042035    .0247845
                CSR_Committee |  -.0076634    .008703    -0.88   0.379    -.0247209    .0093942
        SustainabilityScore_w |  -7.38e-06   .0002177    -0.03   0.973    -.0004342    .0004194

[Frode Andre]

The R-squared is probably negative, you can find information about ivregress on this page:

https://www.stata.com/support/faqs/s...least-squares/

[hussein bataineh]

thanks Frode for guidance, please my question i understand td the case of negative R2 but related to missing R2 im not sure what it is mean ? it is mentioned that R2 has no statistical meaning in the context of 2SLS/IV. .But does missing R2 doe not affect the validity of 2sls results

[Frode Andre]

There is a section in the link that I attached above, called "Is a negative R2 a problem?", therein you may find further information. Also, there is an example of how you can calculate R2 after ivregress.

[hussein bataineh]

actually the R2 in my case appear missing not negative . so there is no explanation for this

[Frode Andre]

Under the section "The short answer", in the link that I sent to you, the second sentence says: "Stata’s ivregress command suppresses the printing of an R2 on 2SLS/IV if the R2 is negative, which is to say, if the model sum of squares is negative."

[hussein bataineh]

Thanks frode , if i use other command for 2SLS can i solve this problem , because i want to report R2 even it is negative

[hussein bataineh]

for example i try to run 2 SLS use ivreg2 but Iveg2 but im not sure what is the code i should run to get R2

ivreg2   hard_final_Exact_new   Firm_Size_w   ROA_four_w   DCAPEX_w TAX_rate_w     Leverage_w     Market_book_four_w   FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w   Governance_Score_w   Fund_St
> atus_w  FUNDING_RATIO_w  Platn_Size_w  Contribut_pension_three_w ACTUAL_RETURN_w  PensionBenefitsDiscountRate_w  CSR_Committee  SustainabilityScore_w   i.year    i.ff_12   (csopresence1 = C
> SO_Percentage )   ,  first endog(csopresence1) robust 

First-stage regressions
-----------------------


First-stage regression of csopresence1:

Statistics robust to heteroskedasticity
Number of obs =                   3059
-----------------------------------------------------------------------------------------------
                              |               Robust
                 csopresence1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------------+----------------------------------------------------------------
               CSO_Percentage |   1.060101   .1166123     9.09   0.000     .8314531    1.288748
                  Firm_Size_w |   .0073951   .0116362     0.64   0.525    -.0154207    .0302108
                   ROA_four_w |   .4802038   .3238439     1.48   0.138    -.1547737    1.115181
                     DCAPEX_w |    .305529    .560944     0.54   0.586    -.7943429    1.405401
                   TAX_rate_w |   .0066612   .0297564     0.22   0.823    -.0516837    .0650061
                   Leverage_w |  -.0038466   .0663292    -0.06   0.954    -.1339018    .1262085
           Market_book_four_w |   .0010832   .0012313     0.88   0.379     -.001331    .0034974
             FREE_CASH_FLOW_w |  -.4811433   .3179622    -1.51   0.130    -1.104588    .1423016
       CASH_FLOW_VOLATILITY_w |   1.968881   .4550355     4.33   0.000      1.07667    2.861093
           Governance_Score_w |   .0000153   .0003888     0.04   0.969    -.0007471    .0007777
                Fund_Status_w |   .2245248   .3368779     0.67   0.505    -.4360092    .8850587
              FUNDING_RATIO_w |   .0435981   .0559566     0.78   0.436    -.0661188    .1533151
                 Platn_Size_w |   .0478488   .0092268     5.19   0.000     .0297573    .0659404
    Contribut_pension_three_w |   .2998949   .1896977     1.58   0.114    -.0720553     .671845
              ACTUAL_RETURN_w |  -.1690191   .1012395    -1.67   0.095    -.3675246    .0294865
PensionBenefitsDiscountRate_w |   .0271159   .0142545     1.90   0.057    -.0008337    .0550655
                CSR_Committee |   .0923577   .0176967     5.22   0.000     .0576588    .1270566
        SustainabilityScore_w |   .0020468   .0004968     4.12   0.000     .0010728    .0030209
                              |
                         year |
                        2007  |  -.0665388    .027278    -2.44   0.015    -.1200241   -.0130535
                        2008  |  -.1235205   .0449569    -2.75   0.006    -.2116699   -.0353711
                        2009  |  -.0988303   .0323657    -3.05   0.002    -.1622913   -.0353693
                        2010  |  -.0961957   .0336954    -2.85   0.004    -.1622641   -.0301273
                        2011  |  -.0940176   .0383868    -2.45   0.014    -.1692845   -.0187506
                        2012  |  -.0572442   .0435397    -1.31   0.189    -.1426148    .0281264
                        2013  |  -.0561397   .0427078    -1.31   0.189    -.1398792    .0275997
                        2014  |  -.0553636   .0486699    -1.14   0.255    -.1507932     .040066
                        2015  |  -.0658538   .0517612    -1.27   0.203    -.1673447    .0356371
                        2016  |  -.0228301   .0557455    -0.41   0.682    -.1321332    .0864729
                        2017  |  -.0406276   .0608709    -0.67   0.505    -.1599803    .0787252
                        2018  |  -.1038641   .0641402    -1.62   0.105     -.229627    .0218988
                        2019  |  -.0872201    .072382    -1.20   0.228    -.2291432     .054703
                        2020  |   -.101147    .082327    -1.23   0.219    -.2625698    .0602759
                        2021  |  -.1478818   .0844054    -1.75   0.080    -.3133799    .0176163
                        2022  |  -.1979142   .1038559    -1.91   0.057    -.4015499    .0057215
                              |
                        ff_12 |
                           2  |   -.063688   .0504452    -1.26   0.207    -.1625985    .0352225
                           3  |  -.0523361   .0363595    -1.44   0.150     -.123628    .0189557
                           4  |  -.1946749   .0524603    -3.71   0.000    -.2975366   -.0918132
                           5  |  -.0209982   .0393319    -0.53   0.593    -.0981182    .0561219
                           6  |   .0542769   .0392218     1.38   0.167    -.0226274    .1311812
                           7  |    .115612   .0666822     1.73   0.083    -.0151353    .2463593
                           8  |  -.0480351   .0415184    -1.16   0.247    -.1294424    .0333721
                           9  |    .040475   .0474909     0.85   0.394    -.0526428    .1335928
                          10  |   .0577808   .0411136     1.41   0.160    -.0228327    .1383943
                          11  |  -.0096359    .042691    -0.23   0.821    -.0933423    .0740705
                          12  |   .0418197    .042227     0.99   0.322     -.040977    .1246165
                              |
                        _cons |  -.7475762   .1303139    -5.74   0.000    -1.003089   -.4920631
-----------------------------------------------------------------------------------------------
F test of excluded instruments:
  F(  1,  3013) =    82.64
  Prob > F      =   0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
  F(  1,  3013) =    82.64
  Prob > F      =   0.0000



Summary results for first-stage regressions
-------------------------------------------

                                           (Underid)            (Weak id)
Variable     | F(  1,  3013)  P-val | SW Chi-sq(  1) P-val | SW F(  1,  3013)
csopresence1 |      82.64    0.0000 |       83.90   0.0000 |       82.64

NB: first-stage test statistics heteroskedasticity-robust

Stock-Yogo weak ID F test critical values for single endogenous regressor:
                                   10% maximal IV size             16.38
                                   15% maximal IV size              8.96
                                   20% maximal IV size              6.66
                                   25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for i.i.d. errors only.

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(1)=75.59    P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                      72.71
Kleibergen-Paap Wald rk F statistic                                82.64

Stock-Yogo weak ID test critical values for K1=1 and L1=1:
                                   10% maximal IV size             16.38
                                   15% maximal IV size              8.96
                                   20% maximal IV size              6.66
                                   25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(1,3013)=      5.33     P-val=0.0210
Anderson-Rubin Wald test           Chi-sq(1)=      5.41     P-val=0.0200
Stock-Wright LM S statistic        Chi-sq(1)=      9.91     P-val=0.0016

NB: Underidentification, weak identification and weak-identification-robust
    test statistics heteroskedasticity-robust

Number of observations               N  =       3059
Number of regressors                 K  =         46
Number of endogenous regressors      K1 =          1
Number of instruments                L  =         46
Number of excluded instruments       L1 =          1

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

                                                      Number of obs =     3059
                                                      F( 45,  3013) =     1.23
                                                      Prob > F      =   0.1377
Total (centered) SS     =  74.11180124                Centered R2   =  -0.0282
Total (uncentered) SS   =           76                Uncentered R2 =  -0.0027
Residual SS             =   76.2031979                Root MSE      =    .1578

-----------------------------------------------------------------------------------------------
                              |               Robust
         hard_final_Exact_new | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
------------------------------+----------------------------------------------------------------
                 csopresence1 |   .1042133   .0459817     2.27   0.023     .0140909    .1943358
                  Firm_Size_w |   -.005251   .0053861    -0.97   0.330    -.0158076    .0053056
                   ROA_four_w |  -.4158489   .1277174    -3.26   0.001    -.6661705   -.1655273
                     DCAPEX_w |  -.0145154   .2138214    -0.07   0.946    -.4335977    .4045669
                   TAX_rate_w |  -.0029006   .0141369    -0.21   0.837    -.0306084    .0248073
                   Leverage_w |  -.0253021    .024828    -1.02   0.308     -.073964    .0233598
           Market_book_four_w |  -.0001865   .0006804    -0.27   0.784      -.00152     .001147
             FREE_CASH_FLOW_w |   .3186146   .1257625     2.53   0.011     .0721247    .5651046
       CASH_FLOW_VOLATILITY_w |  -.0503814   .1943168    -0.26   0.795    -.4312354    .3304725
           Governance_Score_w |   .0003144   .0001643     1.91   0.056    -7.66e-06    .0006364
                Fund_Status_w |  -.3227381   .1731365    -1.86   0.062    -.6620793    .0166032
              FUNDING_RATIO_w |  -.0278129    .022463    -1.24   0.216    -.0718395    .0162138
                 Platn_Size_w |  -.0078465   .0046602    -1.68   0.092    -.0169804    .0012874
    Contribut_pension_three_w |  -.2299897   .0739341    -3.11   0.002    -.3748979   -.0850816
              ACTUAL_RETURN_w |   .0529899   .0508561     1.04   0.297    -.0466862    .1526659
PensionBenefitsDiscountRate_w |    .014494   .0052503     2.76   0.006     .0042035    .0247845
                CSR_Committee |  -.0076634    .008703    -0.88   0.379    -.0247209    .0093942
        SustainabilityScore_w |  -7.38e-06   .0002177    -0.03   0.973    -.0004342    .0004194
                              |
                         year |
                        2007  |      .0053   .0112974     0.47   0.639    -.0168426    .0274425
                        2008  |   .0211131   .0227913     0.93   0.354     -.023557    .0657831
                        2009  |   .0268166    .017553     1.53   0.127    -.0075866    .0612199
                        2010  |   .0143094   .0152084     0.94   0.347    -.0154986    .0441174
                        2011  |   .0112982   .0136692     0.83   0.408    -.0154929    .0380892
                        2012  |   .0298368   .0188988     1.58   0.114    -.0072042    .0668779
                        2013  |   .0126508   .0163083     0.78   0.438    -.0193128    .0446144
                        2014  |   .0251395   .0195377     1.29   0.198    -.0131536    .0634327
                        2015  |   .0308501   .0225179     1.37   0.171    -.0132842    .0749843
                        2016  |   .0067537   .0220942     0.31   0.760    -.0365502    .0500576
                        2017  |   .0130813   .0231749     0.56   0.572    -.0323407    .0585033
                        2018  |   .0283105   .0234347     1.21   0.227    -.0176207    .0742418
                        2019  |   .0061874   .0251403     0.25   0.806    -.0430866    .0554615
                        2020  |   .0363064   .0315524     1.15   0.250    -.0255353     .098148
                        2021  |   .0112083   .0262557     0.43   0.669    -.0402518    .0626685
                        2022  |   .0057365   .0336796     0.17   0.865    -.0602743    .0717472
                              |
                        ff_12 |
                           2  |    .009545   .0241193     0.40   0.692     -.037728    .0568181
                           3  |   .0036317   .0144021     0.25   0.801     -.024596    .0318593
                           4  |   .0552658     .02681     2.06   0.039     .0027191    .1078124
                           5  |   .0006602   .0157348     0.04   0.967    -.0301793    .0314998
                           6  |   .0139097   .0161376     0.86   0.389    -.0177194    .0455387
                           7  |   .0330205   .0308829     1.07   0.285    -.0275089    .0935499
                           8  |   .0141687   .0173244     0.82   0.413    -.0197864    .0481239
                           9  |   .0446592   .0263462     1.70   0.090    -.0069784    .0962969
                          10  |   .0238154    .017521     1.36   0.174    -.0105251     .058156
                          11  |   .0334088   .0205219     1.63   0.104    -.0068133    .0736309
                          12  |   .0076372   .0154415     0.49   0.621    -.0226276     .037902
                              |
                        _cons |   .0464072   .0612628     0.76   0.449    -.0736657    .1664802
-----------------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):             75.592
                                                   Chi-sq(1) P-val =    0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):               72.712
                         (Kleibergen-Paap rk Wald F statistic):         82.643
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                         15% maximal IV size              8.96
                                         20% maximal IV size              6.66
                                         25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.000
                                                 (equation exactly identified)
-endog- option:
Endogeneity test of endogenous regressors:                               4.130
                                                   Chi-sq(1) P-val =    0.0421
Regressors tested:    csopresence1
------------------------------------------------------------------------------
Instrumented:         csopresence1
Included instruments: Firm_Size_w ROA_four_w DCAPEX_w TAX_rate_w Leverage_w
                      Market_book_four_w FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w
                      Governance_Score_w Fund_Status_w FUNDING_RATIO_w
                      Platn_Size_w Contribut_pension_three_w ACTUAL_RETURN_w
                      PensionBenefitsDiscountRate_w CSR_Committee
                      SustainabilityScore_w 2007.year 2008.year 2009.year
                      2010.year 2011.year 2012.year 2013.year 2014.year
                      2015.year 2016.year 2017.year 2018.year 2019.year
                      2020.year 2021.year 2022.year 2.ff_12 3.ff_12 4.ff_12
                      5.ff_12 6.ff_12 7.ff_12 8.ff_12 9.ff_12 10.ff_12 11.ff_12
                      12.ff_12
Excluded instruments: CSO_Percentage
------------------------------------------------------------------------------

[Frode Andre]

The link from post #2 outlines the formula for the R2, and gives an example of how to calculate it following the ivreg 2SLS command.

The information you need is also found by typing

ereturn list

after the ivreg command, see the values of e(rss) and e(mss).

[hussein bataineh]

Thank you very much for guidance please after i run
ereturn list i got

• e(mss): Model Sum of Squares = -2.091396653602786
• e(rss): Residual Sum of Squares = 76.2031978958388

then i use this formula to calculate R2
R2=MSS / ( MSS+RSS)

R2 −2.091396653602786 / ( −2.091396653602786 + 76.2031978958388 )

=-0.0282.


actually this value -0.0282. is the same of Centered R2 when i run ivreg2


please is R2 is the same of Centered R2 in second stage

[Frode Andre]

I do not know this, one is advised not to use R2 in analyses of 2SLS. This is as said in the link in post #2.

I would rather study the postestimation commands available after ivregress available in Stata:.

rivregresspostestimation.pdf (stata.com)

In particular, the

estat firststage

[George Ford]

R2 is essentially meaningless in 2SLS. why would you report it?

You can get a pseudo-R2 by the square of the correlation coefficient between the actual and predicted values.

sysuse auto, clear
ivregress 2sls price (mpg = foreign) headroom
predict yfit, xb
correl yfit price
di "pseudo-R2 = "  %5.3f r(rho)^2