我尝试使用 plm 包进行 gmm 建模。我想使用 Bundell Blond 估计器，并且总是遇到同样的两个警告：
警告信息：
1: In pgmm(log(A) ~ lag(log(A), : the first-step matrix is singular, a general inverse is used 2: In pgmm(log(A) ~ lag(log(A), : the second-step matrix is singular, a general inverse is used
这是我的数据：
data<-structure(list(id = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
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350.709958474795, 352.728232775983, 352.389392036996, 351.490171322274,
350.530952864306, 259.471808586035, 278.701871960409, 296.139045141423,
312.556653326664, 324.786579588327, 334.159209459496, 340.838221191965,
344.783944836434, 347.047072175492, 348.31117919574, 347.406124517167,
344.193009041774, 345.001344520243, 342.828271816297, 345.797039385667,
346.350034479965, 350.709958474795, 352.728232775983, 352.389392036996,
351.490171322274, 350.530952864306, 51.3565239991261, 56.3417951650529,
61.2581743869212, 66.256874264841, 71.4833136332544, 76.5924992094336,
81.6372170972625, 87.3517606104839, 94.4627662209588, 103.390007300147,
113.651627523692, 124.617838469325, 135.655702881477, 146.937641224732,
158.64404432133, 170.16293221615, 180.925104532923, 190.951632309745,
200.554340632463, 209.617127838497, 217.985947769138, 225.678227607646,
232.740532460136, 239.054054078126, 244.518235057184, 248.800119902856,
252.074722206554, 255.003156679698, 258.235704504914, 261.676730230602
), B = c(3690, 3690, 3690, 3690, 3690, 3690, 3690, 3690, 3690,
4672.77, 5087.28, 5535, 6126.63, 5833.89, 6027, 6150, 6273, 1856.2002037284,
6634.10731859754, 13147.6811001334, 20210.8813038618, 26637.6676853087,
31242, 36900, 86100, 184500, 239850, 259530, 273060, 286590,
298890, 319800, 344400, 369000, 393600, 430500, 467400, 516600,
553500, 590400, 627300, 659280, 710940, 735540, 773670, 836400,
931110, 1002450, 1063950, 1125450, 7144.5703125, 23715.9375,
42420.5859375, 55965, 59040, 62730, 67650, 73800, 76260, 79950,
82410, 88560, 76260, 79950, 227.777777777778, 1822.22222222222,
6150, 21871.86, 23268.3231234815, 24057.0270959851, 26383.5,
52053.6, 61440.3222222222, 63716.2777777778, 65067, 66629.1,
74538, 84870, 95940, 107010, 119187, 119187, 150060, 163221,
178350, 210945, 244647, 262482, 282408, 307746, 334560, 358668,
391140, 421890, 451410, 515616, 547350, 608850, 664200, 3690,
9840, 23370, 28290, 30750, 33210, 34440, 52890, 57810, 66420,
76260, 31980, 98400, 115620, 136530, 156210, 167280, 195570,
231240, 277980, 300120, 369000, 461250, 562110, 645750, 740460,
832710, 963090, 1034430, 1109460, 1200480, 1281660, 1313640,
1365300, 1450170, 1504290, 1515360, 1567020, 1635900, 1697400,
1730610, 1792110, 1851150, 456.560625, 2215.23, 6316.05, 18696,
31448.64, 35055, 35297.31, 38772.06, 42312, 47152.05, 56080.62,
68748.39, 85283.28, 104237.58, 133086, 185361, 232273.2, 257316,
230477.4, 275421.6, 305040, 435174, 511557, 596673, 645750, 732711,
821271, 896178, 1019178, 1100481, 1200726, 1299249, 1343160,
1372065, 1398387, 1471449, 1534548, 1582026, 1644510, 1727781,
1786821, 1827411, 1878579, 1944507, 530.4375, 2644.5, 7126.3125,
14760, 30012, 45264, 65067, 84870, 112176, 135300, 159900, 180564,
196800, 218940, 238620, 296184, 324720, 341940, 362850, 33210,
39360, 45099.6138825, 55121.2783881, 76260, 88560, 103320, 176270.07,
189534.39, 202798.71, 217127.595, 231456.48, 234592.98, 237729.48,
243829.05, 249928.62, 257396.565, 264864.51, 279955.38, 286590,
285515.47938, 307005.89178, 314681.039136, 323123.70108, 327652.038084,
340316.031123, 407550.321381, 413997.445101, 455.555555555555,
3644.44444444444, 12300, 36900, 54120, 76260, 114390, 161130,
199260, 269370, 328410, 382530, 420660, 450180, 484620, 517830,
546120, 559650, 569490, 578100, 590400, 603930, 616230, 622380,
630990, 2919.2, 10233.6, 19778.4, 29388.8, 36900, 40134.4444444444,
42275.5555555556, 49200, 67650, 79950, 92250, 104550, 113160,
134070, 150060, 162360, 200859, 221400, 230010, 250920, 279210,
300120, 322260, 334560, 355470, 377610, 397290, 412050, 431730,
448950, 476010, 530130, 538740, 543660, 549810, 552270, 521520,
527670, 528900, 525210, 523980, 522750, 521520, 520290, 523980,
523980, 525210, 8393.52, 29756.16, 58361.04, 88481.28, 114390,
135300, 157440, 207870, 254610, 300120, 356700, 354240, 437880,
521520, 698640, 876990, 1105770, 1273050, 1583010, 1872060, 2285340,
2571274.41, 2841669, 3204396, 3462450, 3756420, 3963060, 4098360,
4218900, 4259490, 4360350, 4412010, 4413240, 4412010, 4409550,
4387410, 4414470, 4414470, 4421850, 4441099.5, 4459980, 4485834.6,
4471050, 4424310, 4399710, 2914.84375, 10420.8333333333, 20660.15625,
31775, 41907.5520833334, 49200, 53283.18359375, 55484.53125,
56491.11328125, 56990, 57668.26171875, 59212.96875, 62311.19140625,
67650, 78239.53125, 89790, 95940, 102090, 109470, 114144, 145140,
174660, 220170, 257070, 282613.41, 308155.59, 333699, 366294,
375150, 378840, 384990, 413280, 426810, 439110, 442800, 461250,
492000, 479700, 485850, 489540, 505530, 468630, 467400, 471520.5,
473550, 500585.4, 504300, 504300, 504300, 1951.91604166667, 6884.17333333333,
13411.535625, 20148.7666666667, 25710.6302083333, 28711.89, 26445,
24600, 23370, 21622.17, 20295, 18361.44, 16605, 15585.33, 14145,
13260.63, 12054, 11439, 11070, 10701, 10332, 636.181197916667,
2343.83333333334, 4821.61921875, 7768.20166666667, 10882.2434895833,
13862.4075, 17177.565, 20492.7225, 24422.88, 30750, 31365, 31980,
33210, 40590, 41820, 43050, 44280, 46740, 50430, 53505, 57810,
61500, 65190, 68880, 75030, 71340, 68880, 67650, 66420, 65190
)), .Names = c("id", "year", "A", "B"), row.names = c(NA, 450L
), class = c("plm.dim", "data.frame"))
这里是我的代码：
library(plm)
data <- plm.data(data, index = c("id", "year"))
z3 <- pgmm(log(A) ~
lag(log(A),1)
+ log(B)
| lag(log(A), 2:99)
, data = data, effect = "twoways", model = "onestep", transformation = "ld")
我在网上找到了 plm 包的代码，第 373 到 407 行是我的错误出现的地方。（因为这两个警告的代码相同，所以我在这里只添加了一个）：
as.vector(x[,1] - crossprod(t(x[,-1]), coefficients)))
outresid <- lapply(residuals,function(x) outer(x,x))
A2 <- mapply(function(x, y) crossprod(t(crossprod(x, y)), x), W, outresid, SIMPLIFY = FALSE)
A2 <- Reduce("+", A2)
minevA2 <- min(eigen(A2)$values)
eps <- 1E-9
if (minevA2 < eps){
A2 <- ginv(A2)
warning("the second-step matrix is singular, a general inverse is used")
}
else A2 <- solve(A2)
可悲的是我不明白，有人可以帮助我了解问题所在以及我如何继续消除此警告吗？