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lately I met a problem that took me quite a long time to figure it out but could not in the end. I want to use pgmm function in the package plm to produce GMM estimate on a cross-section country data including 180 countries and 65 time periods. Here is my code:

pgmm(D_rcr ~ lag(D_rcr,1) +
                eco_cycle + I(log(Human_trend)) + 
                I(log(capital_trend)) + I(log(rtfpna)) + exp_rate + urban + 
                industry + service| plm::lag(mpk3_delta,3:6),data= data_test,
              index = c("country","year"),effect = "twoways",transformation = "ld")

And the data is like: 

          country year         D_rcr     eco_cycle Human_trend capital_trend    rtfpna      exp_rate  urban industry  service
1000 Burkina Faso 1999  0.0074201618  0.0295545705    4.644064     23946.998 0.8284378 -8.221149e-06 17.166 25.19151 42.19550
1001 Burkina Faso 2000 -0.0046062428 -0.0085762554    4.781708     25026.203 0.8177401 -8.013943e-06 17.844 21.52736 45.66413
1002 Burkina Faso 2001 -0.0074698958 -0.0022468581    4.942214     26203.394 0.8430429 -4.433730e-06 18.540 19.47667 43.47496
1003 Burkina Faso 2002 -0.0072339948 -0.0180040290    5.102502     27513.395 0.8564266 -4.243651e-06 19.258 17.52184 43.92530
1004 Burkina Faso 2003  0.0208224248 -0.0013267292    5.262760     28994.841 0.8928111 -4.900598e-06 19.996 21.18051 41.74380
1005 Burkina Faso 2004  0.0077643394 -0.0164384391    5.424015     30686.577 0.9057222 -5.039807e-06 20.757 21.17522 44.30414
1006 Burkina Faso 2005 -0.0162568441  0.0079704026    5.588694     32625.279 0.9540021 -6.000714e-06 21.537 17.97970 42.98950
1007 Burkina Faso 2006  0.0157383040  0.0101814490    5.759905     34843.140 0.9746150 -6.004488e-06 22.339 17.62221 45.65378
1008 Burkina Faso 2007  0.0200791048 -0.0074020766    5.940701     37366.725 0.9920313 -5.925001e-06 23.163 18.95747 48.37608
1009 Burkina Faso 2008 -0.0329526715 -0.0083514921    6.134060     40213.051 1.0026470 -6.737820e-06 23.993 16.22030 43.57783
1010 Burkina Faso 2009  0.0108550329 -0.0364106100    6.341043     43385.046 0.9904070 -5.581967e-06 24.828 19.32466 45.10181
1011 Burkina Faso 2010  0.0003792556 -0.0105232997    6.561223     46865.511 1.0080181 -3.757856e-06 25.665 23.00269 41.38044
1012 Burkina Faso 2011  0.0036570272 -0.0008078762    6.808363     50612.776 1.0000000 -1.947466e-06 26.505 27.15270 39.00203
1013 Burkina Faso 2012 -0.0133615481  0.0088997716    7.066275     54562.488 0.9885733 -4.819380e-06 27.346 24.91152 40.03299
1014 Burkina Faso 2013 -0.0124167169  0.0180233629    7.332700     58635.384 0.9726224 -4.963807e-06 28.186 20.99917 43.38722
1015 Burkina Faso 2014 -0.0093625110  0.0183559642    7.605543     62756.115 0.9531422 -2.547616e-06 29.024 20.47991 44.29216
1016      Burundi 1980 -0.0076063659 -0.0518049023    2.122768      4760.103 0.8508636 -4.026274e-05  4.339 12.61903 25.13108
1017      Burundi 1981  0.0062886770  0.0123692536    2.204532      5003.674 0.9142978 -2.922222e-05  4.503 13.41068 25.27003
1018      Burundi 1982 -0.0073451957 -0.0326804079    2.286727      5257.374 0.8792791 -3.623259e-05  4.674 15.44782 27.69609
1019      Burundi 1983 -0.0048256924 -0.0422295228    2.369051      5513.472 0.8658228 -3.508869e-05  4.850 15.50037 27.25349
1020      Burundi 1984 -0.0083655241 -0.0846945313    2.450960      5763.198 0.8221024 -3.652248e-05  5.033 13.84020 26.02882
1021      Burundi 1985  0.0062427433 -0.0081527185    2.531672      5997.500 0.8820450 -2.695840e-05  5.221 13.00197 25.46080
1022      Burundi 1986  0.0085330972 -0.0050508112    2.610223      6208.165 0.8880036 -2.122831e-05  5.417 13.51567 27.95960
1023      Burundi 1987  0.0013978951  0.0048612717    2.685521      6388.418 0.8895743 -2.379938e-05  5.620 17.12692 27.76170
1024      Burundi 1988  0.0120351151  0.0273960217    2.756473      6533.799 0.9023147 -1.564180e-05  5.830 16.66728 29.08768
1025      Burundi 1989 -0.0040708811  0.0237706740    2.822166      6643.176 0.8862884 -1.854892e-05  6.047 19.66485 26.65657
1026      Burundi 1990  0.0031577402  0.0461310277    2.882089      6718.144 0.9082311 -2.401352e-05  6.271 18.96324 25.15806
1027      Burundi 1991  0.0053723287  0.0913896512    2.944615      6763.149 0.9525304 -2.121296e-05  6.455 19.59612 26.09317
1028      Burundi 1992 -0.0006242234  0.1118378705    3.002747      6784.165 0.9633930 -2.326152e-05  6.637 21.17273 25.29381
1029      Burundi 1993 -0.0140939288  0.0566603249    3.058046      6787.775 0.8787442 -2.704195e-05  6.823 22.44800 24.93331
1030      Burundi 1994 -0.0051914045  0.0446976884    3.112606      6780.856 0.8391036 -2.185189e-05  7.014 22.47806 30.74383
1031      Burundi 1995 -0.0101237974 -0.0044596262    3.168960      6770.888 0.7683206 -2.265241e-05  7.211 19.24821 32.60719
1032      Burundi 1996 -0.0120905700 -0.0733896784    3.230019      6765.241 0.6975604 -1.365663e-05  7.412 12.63033 30.14807
1033      Burundi 1997 -0.0018359105 -0.0465258303    3.298963      6770.493 0.6909751 -9.966291e-06  7.618 15.62753 36.64545
1034      Burundi 1998  0.0010393142  0.0151532770    3.379006      6792.311 0.7113460 -1.557693e-05  7.830 15.84338 36.12517
1035      Burundi 1999 -0.0087320046  0.0148961511    3.473067      6835.203 0.6845708 -1.100638e-05  8.036 16.20578 35.90429
1036      Burundi 2000 -0.0036065995  0.0062503238    3.583363      6902.337 0.6644523 -1.597629e-05  8.246 16.93214 35.00821
1037      Burundi 2001 -0.0015909534  0.0154145281    3.715491      6997.577 0.6616966 -1.724226e-05  8.461 16.49441 37.06893
1038      Burundi 2002  0.0000723279  0.0336641982    3.865710      7124.685 0.6701715 -1.645656e-05  8.682 16.69844 37.51544
1039      Burundi 2003 -0.0081492568 -0.0184660371    4.033378      7286.589 0.6383393 -1.518514e-05  8.908 17.03472 36.60505
1040      Burundi 2004 -0.0053202507 -0.0321812288    4.217188      7484.465 0.6333758 -1.595708e-05  9.139 17.70286 36.85237
1041      Burundi 2005 -0.0073075515 -0.1193560863    4.415421      7718.514 0.5999591 -2.871464e-05  9.375 18.45308 37.05039
1042      Burundi 2006  0.0953559671 -0.1570653899    4.626188      7989.549 0.6067449 -3.880530e-05  9.617 16.71110 38.94535
1043      Burundi 2007  0.0094422379 -0.1988202659    4.847617      8298.925 0.6223342 -3.338575e-05  9.864 18.03837 44.62553
1044      Burundi 2008  0.0217479374 -0.1709468848    5.077926      8647.895 0.6832167 -3.469164e-05 10.118 15.98312 43.42593
1045      Burundi 2009  0.0516023614 -0.0108370357    5.315478      9036.445 0.8509285 -2.165262e-05 10.376 16.63140 42.83632
1046      Burundi 2010  0.0128353068  0.0302280799    5.558862      9461.720 0.9318257 -1.805687e-05 10.641 16.70423 42.84727
1047      Burundi 2011  0.0164302478  0.0549153842    5.820920      9917.799 1.0000000 -1.674949e-05 10.912 16.89924 42.75338
1048      Burundi 2012  0.0177947374  0.0834531229    6.088302     10396.854 1.0781934 -1.448994e-05 11.189 16.88556 42.53204
1049      Burundi 2013 -0.0094655827  0.0443990294    6.360665     10890.133 1.0653062 -1.141332e-05 11.472 17.73397 42.43866
1050      Burundi 2014 -0.0061952542  0.0121767175    6.637850     11389.026 1.0576664 -1.038206e-05 11.761 18.31099 42.42737

The error is 

Error in solve.default(crossprod(WX, t(crossprod(WX, A1)))) : 
      Lapack routine dgesv: system is exactly singular: U[10,10] = 0

And sometimes after adjustments,i.e, data_test <- dplyr::filter(data_test,!is.na(rtfpna)), the error would become:

Error in solve.default(A1) : 
  system is computationally singular: reciprocal condition number = 1.14054e-16

or 

Error in solve.default(crossprod(WX, t(crossprod(WX, A2)))) : 
  system is computationally singular: reciprocal condition number = 1.69599e-24

I guess the pgmm function 1) cannot handle well with the unbalanced dataframe as plm function, especially when the data contains 10% NA. 2)the solve function does not have a substitution to solve inverse matrix when the eigen value is too small. Also, according to my colleague who works mainly on Stata, Stata does not have such problem neither.So my question is, how to fix this problem, is my code heading the right way?

Any suggestion would be helpful.

exteral
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1 Answers1

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Judging from the data you provided, this could cause the error: Your dataset it not balanced. It seems like your data for Burundi starts 1980, while Burkina Faso starts 1999.

I had the same error. In my dataset, I had the years 1891 to 1899, however 1892 was missing - I had forgotten to clean the data, so it is balanced. When I removed 1891, the problem was solved.

Intuitively this makes sense: The Sys-GMM uses high level lags to instrument the first lag. However, if years are randomly missing this obviously does not work consistently.

Of course, it could also be that you have highly correlated vars in your explaining variables.

Constantin Schmidt
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