Dear All,

I am running on Stata 14.0 an ivregress 2sls estimation as in the following code.
Code:
. ivregress 2sls dmbel (rielmbel = gov soc env res dcpi lind dstocks i.code i.time), robust first

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

                                                Number of obs     =      2,747
                                                F( 174,   2572)   =       9.77
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4741
                                                Adj R-squared     =     0.4385
                                                Root MSE          =     0.0850

------------------------------------------------------------------------------
             |               Robust
    rielmbel |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         gov |  -.0056843   .0007252    -7.84   0.000    -.0071063   -.0042622
         soc |  -.0017961   .0006894    -2.61   0.009     -.003148   -.0004443
         env |   .0083121   .0009661     8.60   0.000     .0064177    .0102065
         res |  -.0045355   .0010553    -4.30   0.000    -.0066048   -.0024663
        dcpi |  -.0275036   .0044332    -6.20   0.000    -.0361967   -.0188106
        lind |    -.15713   .0258762    -6.07   0.000    -.2078703   -.1063896
     dstocks |   .0008266   .0004389     1.88   0.060     -.000034    .0016872
             |
        code |
        CHL  |   .0393731    .063514     0.62   0.535    -.0851706    .1639169
        CHN  |   .9101593   .0773214    11.77   0.000     .7585408    1.061778
        COL  |   -.301294   .0476558    -6.32   0.000    -.3947415   -.2078465
        CZE  |   .1136015   .0721176     1.58   0.115    -.0278129     .255016
        HUN  |  -.1895987   .0811023    -2.34   0.019    -.3486312   -.0305662
        IDN  |   .0364302    .025311     1.44   0.150    -.0132017    .0860622
        ISR  |   .0532919   .0848054     0.63   0.530    -.1130019    .2195858
        KOR  |   .4274254   .0463959     9.21   0.000     .3364483    .5184025
        MEX  |   .1617872    .034439     4.70   0.000     .0942562    .2293182
        MYS  |   .1326777   .0602176     2.20   0.028     .0145979    .2507575
        PER  |  -.3035272     .05881    -5.16   0.000     -.418847   -.1882074
        PHL  |  -.2584554   .0476426    -5.42   0.000    -.3518772   -.1650336
        POL  |   .2071764    .056128     3.69   0.000     .0971157    .3172371
        ROU  |  -.2086394   .0610792    -3.42   0.001    -.3284088   -.0888699
        RUS  |   .3532148   .0416844     8.47   0.000     .2714765    .4349532
        THA  |   .1344817   .0526456     2.55   0.011     .0312496    .2377137
        TUR  |   .0960361   .0388248     2.47   0.013     .0199051    .1721672
        ZAF  |   .1614445   .0686339     2.35   0.019     .0268611    .2960278
             |
        time |
        566  |   .0081651   .0540451     0.15   0.880    -.0978112    .1141413
        567  |  -.0018779   .0533686    -0.04   0.972    -.1065276    .1027719
        568  |   .0073689    .054315     0.14   0.892    -.0991367    .1138745
        569  |   .0131488   .0550796     0.24   0.811     -.094856    .1211535
        570  |   .0035239   .0526657     0.07   0.947    -.0997476    .1067955
        571  |  -.0417565   .0453115    -0.92   0.357    -.1306073    .0470943
        572  |  -.0351463    .045288    -0.78   0.438    -.1239509    .0536583
        573  |  -.0181831   .0485004    -0.37   0.708    -.1132868    .0769207
        574  |  -.0039052   .0499676    -0.08   0.938     -.101886    .0940755
        575  |  -.0285183   .0465499    -0.61   0.540    -.1197973    .0627608
        576  |  -.0143531   .0488801    -0.29   0.769    -.1102014    .0814952
        577  |   -.068227   .0438727    -1.56   0.120    -.1542564    .0178024
        578  |    -.08955   .0430002    -2.08   0.037    -.1738686   -.0052315
        579  |  -.1002657   .0420257    -2.39   0.017    -.1826734    -.017858
        580  |    -.05097   .0442849    -1.15   0.250    -.1378076    .0358676
        581  |  -.0502664   .0438877    -1.15   0.252    -.1363253    .0357925
        582  |  -.0913523    .042259    -2.16   0.031    -.1742173   -.0084872
        583  |    -.08904   .0439348    -2.03   0.043    -.1751913   -.0028888
        584  |  -.0976524   .0438337    -2.23   0.026    -.1836054   -.0116994
        585  |    -.14857   .0462526    -3.21   0.001     -.239266    -.057874
        586  |  -.3533309   .0547859    -6.45   0.000    -.4607599   -.2459019
        587  |  -.3797358   .0544885    -6.97   0.000    -.4865817     -.27289
        588  |  -.3462651   .0517457    -6.69   0.000    -.4477327   -.2447976
        589  |  -.3553977   .0476362    -7.46   0.000    -.4488069   -.2619885
        590  |  -.4102855   .0509847    -8.05   0.000    -.5102608   -.3103102
        591  |  -.3337814   .0460526    -7.25   0.000    -.4240852   -.2434775
        592  |  -.2324673   .0415684    -5.59   0.000    -.3139783   -.1509563
        593  |  -.1843035   .0421199    -4.38   0.000    -.2668959    -.101711
        594  |  -.1558125   .0424002    -3.67   0.000    -.2389546   -.0726705
        595  |  -.1271502   .0433097    -2.94   0.003    -.2120757   -.0422247
        596  |  -.1174798   .0435129    -2.70   0.007    -.2028037   -.0321559
        597  |  -.1053721   .0447938    -2.35   0.019    -.1932077   -.0175365
        598  |  -.1093318   .0434922    -2.51   0.012     -.194615   -.0240485
        599  |  -.1337709   .0408405    -3.28   0.001    -.2138544   -.0536873
        600  |  -.1107745   .0410948    -2.70   0.007    -.1913568   -.0301922
        601  |  -.1310213   .0413355    -3.17   0.002    -.2120755   -.0499672
        602  |  -.1349439   .0401814    -3.36   0.001     -.213735   -.0561528
        603  |  -.1136856    .040691    -2.79   0.005     -.193476   -.0338952
        604  |  -.1125739   .0415963    -2.71   0.007    -.1941396   -.0310083
        605  |  -.1450647   .0436493    -3.32   0.001     -.230656   -.0594734
        606  |  -.1481128   .0429361    -3.45   0.001    -.2323056   -.0639199
        607  |  -.1345606   .0461171    -2.92   0.004    -.2249911   -.0441301
        608  |  -.1421602   .0444082    -3.20   0.001    -.2292397   -.0550807
        609  |  -.1279889   .0423831    -3.02   0.003    -.2110974   -.0448804
        610  |   -.110785   .0429728    -2.58   0.010    -.1950499   -.0265202
        611  |   -.133421   .0418201    -3.19   0.001    -.2154253   -.0514166
        612  |  -.1118164   .0430845    -2.60   0.010    -.1963003   -.0273325
        613  |  -.1248219   .0419105    -2.98   0.003    -.2070036   -.0426401
        614  |  -.1235164   .0405959    -3.04   0.002    -.2031203   -.0439125
        615  |   -.123387   .0399894    -3.09   0.002    -.2018018   -.0449723
        616  |  -.1215721   .0400539    -3.04   0.002    -.2001134   -.0430309
        617  |  -.1318429   .0397651    -3.32   0.001    -.2098178    -.053868
        618  |  -.1403435   .0395989    -3.54   0.000    -.2179925   -.0626945
        619  |   -.137319   .0408709    -3.36   0.001    -.2174621   -.0571758
        620  |  -.1846433   .0424692    -4.35   0.000    -.2679206   -.1013659
        621  |  -.2501755   .0436816    -5.73   0.000    -.3358301   -.1645209
        622  |  -.2015664   .0417181    -4.83   0.000    -.2833709   -.1197619
        623  |  -.2395515   .0440191    -5.44   0.000     -.325868    -.153235
        624  |  -.2306571   .0431127    -5.35   0.000    -.3151963   -.1461179
        625  |  -.2230069   .0424552    -5.25   0.000    -.3062568   -.1397571
        626  |  -.1901461    .040798    -4.66   0.000    -.2701464   -.1101459
        627  |  -.1763518   .0416542    -4.23   0.000     -.258031   -.0946727
        628  |  -.1941324   .0431574    -4.50   0.000    -.2787592   -.1095055
        629  |  -.2383907   .0453307    -5.26   0.000    -.3272791   -.1495023
        630  |   -.205805   .0418966    -4.91   0.000    -.2879595   -.1236504
        631  |  -.1746416   .0412912    -4.23   0.000     -.255609   -.0936742
        632  |  -.1599838   .0409211    -3.91   0.000    -.2402255   -.0797421
        633  |  -.1301993   .0405216    -3.21   0.001    -.2096576    -.050741
        634  |  -.1302085   .0404654    -3.22   0.001    -.2095565   -.0508605
        635  |  -.1220317   .0404359    -3.02   0.003     -.201322   -.0427414
        636  |  -.1054495   .0400379    -2.63   0.008    -.1839592   -.0269398
        637  |  -.1181236   .0398405    -2.96   0.003    -.1962463   -.0400008
        638  |  -.1194951   .0402626    -2.97   0.003    -.1984455   -.0405447
        639  |  -.1323093   .0406713    -3.25   0.001    -.2120611   -.0525575
        640  |  -.1152404   .0400866    -2.87   0.004    -.1938457   -.0366351
        641  |  -.1202925   .0407074    -2.96   0.003    -.2001151   -.0404699
        642  |   -.162043   .0411493    -3.94   0.000    -.2427322   -.0813539
        643  |  -.1661865   .0417703    -3.98   0.000    -.2480934   -.0842797
        644  |  -.1807564   .0433515    -4.17   0.000    -.2657639    -.095749
        645  |  -.1551145    .041657    -3.72   0.000    -.2367992   -.0734298
        646  |   -.142005   .0419176    -3.39   0.001    -.2242007   -.0598093
        647  |  -.1529248   .0430962    -3.55   0.000    -.2374315    -.068418
        648  |  -.1507832   .0433217    -3.48   0.001    -.2357321   -.0658343
        649  |  -.1651797     .04394    -3.76   0.000    -.2513412   -.0790183
        650  |  -.1390598   .0411616    -3.38   0.001    -.2197729   -.0583466
        651  |    -.14292    .040973    -3.49   0.000    -.2232634   -.0625765
        652  |  -.1309518   .0410339    -3.19   0.001    -.2114146   -.0504889
        653  |  -.1148193   .0405231    -2.83   0.005    -.1942806   -.0353581
        654  |  -.1123831   .0408201    -2.75   0.006    -.1924268   -.0323395
        655  |  -.1212662   .0409699    -2.96   0.003    -.2016036   -.0409287
        656  |  -.1097958    .040625    -2.70   0.007    -.1894569   -.0301347
        657  |  -.1195196   .0413159    -2.89   0.004    -.2005353   -.0385038
        658  |  -.1135709   .0407567    -2.79   0.005    -.1934902   -.0336516
        659  |  -.1042169   .0409735    -2.54   0.011    -.1845613   -.0238726
        660  |  -.1255047   .0416624    -3.01   0.003       -.2072   -.0438095
        661  |  -.1425736   .0431596    -3.30   0.001    -.2272046   -.0579425
        662  |   -.117195   .0425727    -2.75   0.006    -.2006751   -.0337148
        663  |  -.1348688   .0435859    -3.09   0.002    -.2203358   -.0494018
        664  |  -.1280062   .0429813    -2.98   0.003    -.2122876   -.0437247
        665  |  -.1289821   .0431838    -2.99   0.003    -.2136607   -.0443035
        666  |  -.1323969     .04368    -3.03   0.002    -.2180484   -.0467454
        667  |   -.143292   .0440901    -3.25   0.001    -.2297477   -.0568363
        668  |  -.1713126   .0463701    -3.69   0.000    -.2622391   -.0803861
        669  |  -.2094114   .0526716    -3.98   0.000    -.3126944   -.1061283
        670  |  -.1659607    .047872    -3.47   0.001    -.2598324    -.072089
        671  |  -.1628071   .0478387    -3.40   0.001    -.2566134   -.0690008
        672  |  -.1601802   .0459658    -3.48   0.001    -.2503139   -.0700466
        673  |  -.1784725   .0474774    -3.76   0.000    -.2715702   -.0853747
        674  |   -.188288   .0470512    -4.00   0.000      -.28055   -.0960261
        675  |  -.1389032   .0445062    -3.12   0.002    -.2261747   -.0516316
        676  |  -.1319502   .0442777    -2.98   0.003    -.2187738   -.0451266
        677  |  -.1320015   .0436834    -3.02   0.003    -.2176596   -.0463434
        678  |  -.1142698   .0429019    -2.66   0.008    -.1983956    -.030144
        679  |  -.1127285   .0422778    -2.67   0.008    -.1956304   -.0298266
        680  |  -.0896584   .0420153    -2.13   0.033    -.1720456   -.0072712
        681  |    -.09995   .0430073    -2.32   0.020    -.1842824   -.0156177
        682  |  -.1025734   .0427267    -2.40   0.016    -.1863557   -.0187911
        683  |  -.1245426   .0423403    -2.94   0.003     -.207567   -.0415181
        684  |  -.1034273   .0416639    -2.48   0.013    -.1851255    -.021729
        685  |  -.0970144    .042589    -2.28   0.023    -.1805266   -.0135022
        686  |  -.0844257   .0421653    -2.00   0.045     -.167107   -.0017444
        687  |   -.075377   .0430377    -1.75   0.080    -.1597691    .0090152
        688  |   -.071149   .0430912    -1.65   0.099     -.155646     .013348
        689  |  -.0723727   .0428111    -1.69   0.091    -.1563205    .0115751
        690  |  -.0663081   .0416831    -1.59   0.112    -.1480439    .0154277
        691  |  -.0541647   .0410407    -1.32   0.187    -.1346408    .0263114
        692  |  -.0431412   .0416508    -1.04   0.300    -.1248138    .0385313
        693  |  -.0461507   .0423142    -1.09   0.276    -.1291241    .0368226
        694  |  -.0477742   .0430899    -1.11   0.268    -.1322686    .0367202
        695  |  -.0433186   .0439681    -0.99   0.325    -.1295351    .0428979
        696  |  -.0432889    .042812    -1.01   0.312    -.1272384    .0406607
        697  |  -.0307226   .0435008    -0.71   0.480    -.1160229    .0545776
        698  |  -.0407607   .0434061    -0.94   0.348    -.1258752    .0443538
        699  |  -.0391918   .0442075    -0.89   0.375    -.1258778    .0474942
        700  |   -.041366   .0440631    -0.94   0.348    -.1277688    .0450369
        701  |  -.0579426   .0439573    -1.32   0.188    -.1441379    .0282526
        702  |  -.0648714   .0447735    -1.45   0.147    -.1526671    .0229243
        703  |  -.0469431   .0443466    -1.06   0.290    -.1339017    .0400156
        704  |   -.078142   .0429083    -1.82   0.069    -.1622804    .0059963
        705  |   -.060707   .0430631    -1.41   0.159    -.1451488    .0237349
        706  |  -.0827343   .0445174    -1.86   0.063    -.1700279    .0045593
        707  |  -.0747965    .044787    -1.67   0.095    -.1626186    .0130256
        708  |  -.0777714   .0442149    -1.76   0.079    -.1644718     .008929
        709  |  -.0472163   .0449729    -1.05   0.294     -.135403    .0409704
        710  |  -.0371848   .0455833    -0.82   0.415    -.1265684    .0521988
        711  |  -.0577427   .0431851    -1.34   0.181    -.1424238    .0269383
        712  |  -.0428744   .0435946    -0.98   0.325    -.1283585    .0426097
        713  |  -.0706304   .0436904    -1.62   0.106    -.1563024    .0150415
        714  |  -.0501905   .0446396    -1.12   0.261    -.1377236    .0373426
             |
       _cons |   3.718266   .6176449     6.02   0.000     2.507135    4.929398
------------------------------------------------------------------------------


Instrumental variables (2SLS) regression          Number of obs   =      2,747
                                                  Wald chi2(1)    =      18.52
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.0317
                                                  Root MSE        =     .04316

------------------------------------------------------------------------------
             |               Robust
       dmbel |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    rielmbel |   .0618787   .0143775     4.30   0.000     .0336994     .090058
       _cons |   .0007128   .0008038     0.89   0.375    -.0008626    .0022882
------------------------------------------------------------------------------
Instrumented:  rielmbel
Instruments:   gov soc env res dcpi lind dstocks 2.code 3.code 4.code 5.code
               6.code 7.code 8.code 9.code 10.code 11.code 12.code 13.code
               14.code 15.code 16.code 17.code 18.code 19.code 566.time
               567.time 568.time 569.time 570.time 571.time 572.time
               573.time 574.time 575.time 576.time 577.time 578.time
               579.time 580.time 581.time 582.time 583.time 584.time
               585.time 586.time 587.time 588.time 589.time 590.time
               591.time 592.time 593.time 594.time 595.time 596.time
               597.time 598.time 599.time 600.time 601.time 602.time
               603.time 604.time 605.time 606.time 607.time 608.time
               609.time 610.time 611.time 612.time 613.time 614.time
               615.time 616.time 617.time 618.time 619.time 620.time
               621.time 622.time 623.time 624.time 625.time 626.time
               627.time 628.time 629.time 630.time 631.time 632.time
               633.time 634.time 635.time 636.time 637.time 638.time
               639.time 640.time 641.time 642.time 643.time 644.time
               645.time 646.time 647.time 648.time 649.time 650.time
               651.time 652.time 653.time 654.time 655.time 656.time
               657.time 658.time 659.time 660.time 661.time 662.time
               663.time 664.time 665.time 666.time 667.time 668.time
               669.time 670.time 671.time 672.time 673.time 674.time
               675.time 676.time 677.time 678.time 679.time 680.time
               681.time 682.time 683.time 684.time 685.time 686.time
               687.time 688.time 689.time 690.time 691.time 692.time
               693.time 694.time 695.time 696.time 697.time 698.time
               699.time 700.time 701.time 702.time 703.time 704.time
               705.time 706.time 707.time 708.time 709.time 710.time
               711.time 712.time 713.time 714.time

. estat overid

  Test of overidentifying restrictions:

  Score chi2(173)        =  788.538  (p = 0.0000)

. estat endogenous

  Tests of endogeneity
  Ho: variables are exogenous

  Robust score chi2(1)            =  .831163  (p = 0.3619)
  Robust regression F(1,2744)     =  .831294  (p = 0.3620)

.
end of do-file

.
I am working with monthly panel data from 2007 to 2020 for 19 countries. The dependent variable dmbel is the first difference in CDS spread (S_it – S_it-1). The independent endogenous variable rielmbel is the difference between a forecast of expected losses for the next period and the CDS spread in the previous period (R_it+1 – S_it-1). The instruments are a set of economic fundamentals (all measured at time t) and country and year dummies (i.code and i.time, respectively).

I would like to ask you three questions, please.
  1. Is including time dummies in the first step a legitimate choice? If omitted, the second step regression would lose significance. However, I am not sure about the theoretical soundness of this approach.
  2. The estat overid test rejects the null hypothesis of exogenous instruments. Given the large number of instruments, I suspect many of them are actually endogenous, but some may not. So how can I test for exogeneity on a subset of instruments?
  3. The estat endogenous test fails to reject the null hypothesis of exogenous independent variable, so that OLS would be more efficient than 2SLS. However, I know that the endogeneity test is only meaningful in the presence of valid instruments. Since the test of overidentifying restrictions rejects the null of exogenous instruments, I would conclude I am not allowed to opt for OLS. Please can you confirm my interpretation is correct? (Below the output of the OLS regression for comparison purposes.)
Code:
. reg dmbel rielmbel, robust

Linear regression                               Number of obs     =      2,968
                                                F(1, 2966)        =      30.56
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0349
                                                Root MSE          =     .04341

------------------------------------------------------------------------------
             |               Robust
       dmbel |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    rielmbel |   .0728101   .0131701     5.53   0.000     .0469865    .0986336
       _cons |   .0010476    .000795     1.32   0.188    -.0005113    .0026065
------------------------------------------------------------------------------

.
end of do-file

.
Any help will be greatly appreciated. Thanks in advance.

Best,

Daniele Veggiato