Translating xtabond call from Stata to R

Question

I am trying to replicate findings from a particular study. The study uses the xtabond command in Stata to run an Arellano-Bond estimator with lags of the dependent variables. The goal of the study is to estimate the effects of being in year X of a 4 year cycle (with the cycle repeating over a 50 year period) for N units.

The call in Stata is:

xtabond rpcexp_annual election election_3 election_2 rpcinc_annual rpcgrants_annual unem popmillions_annual kidsaged rr dd y1974 y1975 y1976 y1977 y1978 y1979 y1980 y1981 y1982 y1983 y1984 y1985 y1986 if stcode!=2 & stcode!=4 & stcode!=29 & stcode!=39 & stcode!=45 & stcode!=42 & year>=1974, robust maxlag(4)

We have tried several packages in R including pgmm but have been unable to replicate the results (our understanding is pgmm may be bugged as described here). We have two questions.

First, which function in R will allow us to replicate this command?

Second, what does the lag notation refer to in the initial Stata command? It is unclear from the documentation what is being lagged as there is no division between exogenous and endogenous variables or instruments.

Data attached for a reproducible example:

    * Example generated by -dataex-. To install: ssc install dataex
    clear
    input float rpcexp_annual byte(election election_3 election_2) float(rpcinc_annual rpcgrants_annual unem popmillions_annual kidsaged) byte(rr dd y1974 y1975 y1976 y1978 y1979 y1980 y1981 y1982 y1983 y1984 y1985 y1986)
    1316.5624 0 0 1  9125.947  288.6954    . 3.267  35.42777 . . 0 0 0 0 0 0 0 0 0 0 0 0
    1376.9705 0 0 0  9413.523 308.77295    . 3.316 35.628387 . . 0 0 0 0 0 0 0 0 0 0 0 0
    1400.4978 1 0 0  9797.964 299.67462    . 3.323  35.90664 . . 0 0 0 0 0 0 0 0 0 0 0 0
      1495.06 0 1 0 10348.486   336.344    . 3.358  35.97399 . . 0 0 0 0 0 0 0 0 0 0 0 0
    1645.6897 0 0 1  10948.69  381.1924    . 3.395  36.14107 . . 0 0 0 0 0 0 0 0 0 0 0 0
    1803.7977 0 0 0  11418.86  477.7399    . 3.443 35.740902 . . 0 0 0 0 0 0 0 0 0 0 0 0
    1956.1627 1 0 0 11752.167  468.3919    . 3.464 35.687828 . . 0 0 0 0 0 0 0 0 0 0 0 0
    2041.5275 0 1 0  12293.09  471.9064    . 3.458  36.63967 . . 0 0 0 0 0 0 0 0 0 0 0 0
      2120.65 0 0 1 12711.763  490.5691  4.5 3.446  36.79629 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    2215.6824 0 0 0 13060.082 560.79626  3.9  3.44  36.51686 0 1 0 0 0 0 0 0 0 0 0 0 0 0
     2350.494 1 0 0 13499.014  635.9165  5.9 3.444 36.453197 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    2441.2668 0 1 0 14287.498  689.6812  5.5 3.497 36.071228 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    2446.2986 0 0 1  15086.62  668.4541  4.5 3.539  35.72848 0 1 0 0 0 0 0 0 0 0 0 0 0 0
     2451.418 0 0 0  15173.22   679.898  4.5  3.58  35.42019 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    2564.1316 1 0 0 15227.479  699.0737  5.5 3.626  35.07692 0 1 1 0 0 0 0 0 0 0 0 0 0 0
     2718.576 0 1 0  15877.83  748.5618  7.7 3.679  34.79945 0 1 0 1 0 0 0 0 0 0 0 0 0 0
    2813.7976 0 0 1 16376.425  800.3513  6.8 3.735 34.758896 0 1 0 0 1 0 0 0 0 0 0 0 0 0
     2832.032 0 0 0 16924.018  800.6426  7.4  3.78  35.31165 0 1 0 0 0 0 0 0 0 0 0 0 0 0
     2824.152 1 0 0 16975.473  802.2593  6.3 3.832  35.08583 0 1 0 0 0 1 0 0 0 0 0 0 0 0
      2782.23 0 1 0 16537.809  793.6146  7.1 3.866  34.65111 0 1 0 0 0 0 1 0 0 0 0 0 0 0
      2736.76 0 0 1 16428.512  740.1887  8.8 3.894  33.53878 0 1 0 0 0 0 0 1 0 0 0 0 0 0
     2794.776 0 0 0  16380.41  656.3935 10.7 3.919  33.00229 0 1 0 0 0 0 0 0 1 0 0 0 0 0
      2881.61 1 0 0  16777.41  625.9977 14.4 3.925  32.70743 0 1 0 0 0 0 0 0 0 1 0 0 0 0
     2908.602 0 1 0  17656.92   640.411 13.7 3.934   32.4413 0 1 0 0 0 0 0 0 0 0 1 0 0 0
     3107.953 0 0 1 18356.063  695.7643 11.1 3.952  32.33893 0 1 0 0 0 0 0 0 0 0 0 1 0 0
     3309.771 0 0 0 18958.783  704.9506  8.9 3.973  32.34709 0 1 0 0 0 0 0 0 0 0 0 0 1 0
    3230.8005 1 0 0 19360.621   664.225  9.8 3.992  32.44691 0 1 0 0 0 0 0 0 0 0 0 0 0 1
    3279.5334 0 1 0  19815.21  736.0481  7.8 4.015 32.532257 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    3394.6855 0 0 1  20468.39  698.1594  7.2 4.024  32.38347 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     3514.046 0 0 0  20736.43  719.9347    7  4.03  32.39437 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     3669.283 1 0 0 20748.943  773.0032  6.9  4.04  33.16011 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     3877.976 0 1 0  21135.86  838.7319  7.2 4.099   31.8731 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    3900.5786 0 0 1 21194.834  902.0014  7.4 4.154  31.80135 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     3996.209 0 0 0  21507.75  904.3861  7.6 4.214  31.50653 0 1 0 0 0 0 0 0 0 0 0 0 0 0
     4111.263 1 0 0  21879.33  914.1227    6  4.26  31.47955 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    4186.5776 0 1 0  22021.05  916.8386  6.3 4.297  31.27467 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     4228.099 0 0 1  22351.08  934.7521  5.1 4.331  31.18011 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    4401.7114 0 0 0  23063.37  1014.215  5.1 4.368  31.03124 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     4634.854 1 0 0  23431.49 1073.6261  4.2 4.405  31.23361 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     4894.457 0 1 0  23716.32 1129.3009  4.8  4.43  30.73455 0 1 0 0 0 0 0 0 0 0 0 0 0 0
            . 0 0 1         .         .  4.5 4.447  31.60606 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    2311.1653 0 0 1  16617.84  847.2505    .  .226         . . . 0 0 0 0 0 0 0 0 0 0 0 0
    2852.0886 0 0 0  16158.52  929.4943    .  .238         . . . 0 0 0 0 0 0 0 0 0 0 0 0
     3365.185 1 0 0 16487.813 1113.9612    .  .246         . . . 0 0 0 0 0 0 0 0 0 0 0 0
    3939.2825 0 1 0 17478.406 1547.7615    .  .256         . . . 0 0 0 0 0 0 0 0 0 0 0 0
     4497.172 0 0 1 18493.336  2104.962    .  .263         . . . 0 0 0 0 0 0 0 0 0 0 0 0
    4830.5137 0 0 0 19254.928 2135.0315    .  .271         . . . 0 0 0 0 0 0 0 0 0 0 0 0
     5464.552 1 0 0  20194.69 2389.3037    .  .271         . . . 0 0 0 0 0 0 0 0 0 0 0 0
     5894.966 0 1 0  20868.88 2505.1936    .  .278         . . . 0 0 0 0 0 0 0 0 0 0 0 0
     5609.474 0 0 1  21730.25  1989.375    .  .285         . 1 0 0 0 0 0 0 0 0 0 0 0 0 0
     5705.096 0 0 0  22923.81 1670.6044    .  .296         . 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      6835.52 1 0 0  23653.85 1864.8027    .  .303         . 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     8433.653 0 1 0  24286.54  2188.944    .  .316         . 0 1 0 0 0 0 0 0 0 0 0 0 0 0
     9179.755 0 0 1 25687.615 2311.7124    .  .324         . 0 1 0 0 0 0 0 0 0 0 0 0 0 0
    8912.5205 0 0 0 27708.854 2321.8918    .  .331         . 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     8486.839 1 0 0   31254.2 2227.4233    .  .341         . 0 0 1 0 0 0 0 0 0 0 0 0 0 0
     8607.662 0 1 0 34856.113 2262.1702    .  .376         . 0 0 0 1 0 0 0 0 0 0 0 0 0 0
     9146.642 0 0 1 35365.742 2262.9238    8  .401  28.92051 0 0 0 0 1 0 0 0 0 0 0 0 0 0
     9563.523 0 0 0  33771.79  2229.545  9.4  .403        29 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    10327.962 1 0 0  32091.33 2159.0454 11.2  .405      28.3 0 0 0 0 0 1 0 0 0 0 0 0 0 0
    11982.192 0 1 0  31357.47 2150.9333  9.2  .403      27.9 0 0 0 0 0 0 1 0 0 0 0 0 0 0
    13077.068 0 0 1 31373.104 2173.8315  9.7  .402      25.8 0 0 0 0 0 0 0 1 0 0 0 0 0 0
     13513.48 0 0 0   32238.6 1904.3528  9.3  .418      25.1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
     14328.63 1 0 0  33115.49 1655.2924  9.9   .45      24.7 0 0 0 0 0 0 0 0 0 1 0 0 0 0
    14726.245 0 1 0  32742.28  1599.464 10.3  .488      24.3 0 0 0 0 0 0 0 0 0 0 1 0 0 0
    14798.727 0 0 1   32428.8  1584.992   10  .514      24.3 0 0 0 0 0 0 0 0 0 0 0 1 0 0
    14743.357 0 0 0  31843.23  1483.284  9.7  .532      24.3 0 0 0 0 0 0 0 0 0 0 0 0 1 0
    14645.305 1 0 0 30247.625 1473.2877 10.8  .544      24.2 0 0 0 0 0 0 0 0 0 0 0 0 0 1
     14073.73 0 1 0 29168.084 1855.4728 10.8  .539      24.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    13384.085 0 0 1  29509.66  1938.952  9.3  .542      24.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    13105.982 0 0 0 30133.895  1718.062  6.7  .547        25 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    12707.703 1 0 0  29759.19 1746.5212    7   .55      25.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    12542.252 0 1 0  29238.13  1781.084  8.7   .57      25.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    12372.348 0 0 1   29222.5  1893.831  9.2  .589      26.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    12137.702 0 0 0 29192.496  1971.333  7.7  .599      26.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    11982.547 1 0 0  28979.56 1981.7893  7.8  .603  27.04224 0 0 0 0 0 0 0 0 0 0 0 0 0 0
      11708.7 0 1 0   28569.2  2025.486  7.3  .604  27.41656 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    11633.382 0 0 1 28504.266 2068.8638  7.8  .609  27.44053 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    11718.472 0 0 0  28909.61 2123.8718  7.9  .613   28.1243 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    11835.538 1 0 0 29073.613 2205.6846  5.8   .62   28.7899 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    12135.523 0 1 0   29462.7 2265.7112  6.4  .625  29.30968 0 0 0 0 0 0 0 0 0 0 0 0 0 0
            . 0 0 1         .         .  6.7  .627  28.52963 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    1880.2672 1 . . 12130.445  289.0184    . 1.302 33.343147 . . 0 0 0 0 0 0 0 0 0 0 0 0
     1994.296 0 . . 12234.726 303.12503    . 1.407 33.878998 . . 0 0 0 0 0 0 0 0 0 0 0 0
    2069.7703 1 . . 12379.693  328.9912    . 1.471  34.31105 . . 0 0 0 0 0 0 0 0 0 0 0 0
    2125.8398 0 . . 12616.122   340.135    . 1.521  34.67369 . . 0 0 0 0 0 0 0 0 0 0 0 0
     2231.752 1 . . 13008.673  390.7931    . 1.556  35.24855 . . 0 0 0 0 0 0 0 0 0 0 0 0
     2390.786 0 . .   13467.5  471.8137    . 1.584  35.30158 . . 0 0 0 0 0 0 0 0 0 0 0 0
     2599.287 1 . . 13973.276  537.7237    . 1.614  35.93263 . . 0 0 0 0 0 0 0 0 0 0 0 0
     2677.664 0 . .  14748.19   558.815    . 1.646  35.84447 . . 0 0 0 0 0 0 0 0 0 0 0 0
     2640.892 1 . .  15805.41 524.65796  3.6 1.682  36.26635 1 0 0 0 0 0 0 0 0 0 0 0 0 0
    2717.9175 0 . .  16762.72  522.0126  2.9 1.737  35.73829 1 0 0 0 0 0 0 0 0 0 0 0 0 0
     2854.258 1 0 0 17413.816  531.3039  4.1 1.775 36.049107 1 0 0 0 0 0 0 0 0 0 0 0 0 0
     3042.169 0 1 0 18050.035  531.0124  4.5 1.896   37.0985 1 0 0 0 0 0 0 0 0 0 0 0 0 0
     3121.365 0 0 1 18783.205 571.12964  3.8 2.008 35.863472 1 0 0 0 0 0 0 0 0 0 0 0 0 0
     3047.864 0 0 0 18822.143  584.3438  3.6 2.124  34.97347 1 0 0 0 0 0 0 0 0 0 0 0 0 0
    3112.0754 1 0 0 18161.543  576.8924  5.6 2.223  34.81687 1 0 1 0 0 0 0 0 0 0 0 0 0 0
    3286.8125 0 1 0 18074.033  610.4025 12.1 2.285   34.6745 0 0 0 1 0 0 0 0 0 0 0 0 0 0
     3390.967 0 0 1 18615.066  624.2149  9.8 2.346 33.973885 0 0 0 0 1 0 0 0 0 0 0 0 0 0
     3370.134 0 0 0 19383.855  654.8785  8.2 2.425 35.583622 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    end

The result of this gmm should be:

Please help reproduce this result in R.

Answer 1

This option says to use at most lag 4 to instrument for both predetermined and endogenous variables.

If you want to treat variables differently, you would use pre(varlist [, lagstruct(prelags, premaxlags)]) and endogenous(varlist [, lagstruct(endlags, endmaxlags)]).

You can let each variable have its own lag structure by repeating options (or have groups of variables that are treated similarly):

webuse abdata
xtabond n l(0/2).ys yr1980-yr1984, lags(2) endogenous(w, lag(1,4)) endogenous(k, lag(2,3))

In R, I would try the plm package for this. It looks like you already ruled this out, and I am unsure if there is anything better. Let me offer my strategy for solving such problems instead.

First, try installing the dev version of plm. Sometimes that works if the version on CRAN is stale.

Second, ensure your summary stats match the authors to rule out data issues.

Third, I would also not consider anything buggy because some user on SO reported that while there are no issues on GitHub. These models can be finicky in any language. Try replicating the simplest model on a public dataset and then increase complexity in a direction similar to what you are trying to do until you get a divergence between R and Stata. If you cannot figure that out, submit a bug request on GitHub with a reproducible example. Cameron and Trivedi's MUS have many examples and accessible data in Stata. The first edition is cheap if you cannot get the second edition from the library. I think the Baltagi and Hsiao panel data books may also have some reproducible examples.

I would also try replicating the Stata code using the same version of the package the authors used and then the newest one. Sometimes there are bug fixes, so you are trying to replicate something that was itself buggy in the same language, which may be impossible. This relies on having access to Stata, maybe even an older version.