The TOJ bias-corrected estimation of the moments
tojmoment.RdThe `tojmoment()` function enables to implement the TOJ bias-corrected estimation of the moments of the heterogeneous mean, the heterogeneous autocovariance, and the heterogeneous autocorrelation. The method is developed by Okui and Yanagi (2019). For more details, see the package vignette with `vignette("panelhetero")`.
Arguments
- data
A matrix of panel data. Each row corresponds to individual time series.
- acov_order
A non-negative integer of the order of autocovariance. Default is 0.
- acor_order
A positive integer of the order of autocorrelation Default is 1.
- R
A positive integer of the number of bootstrap repetitions. Default is 1000.
Value
A list that contains the following elements.
- estimate
A vector of the parameter estimates
- se
A vector of the standard errors
- ci
A matrix of the 95 percent confidence intervals
- quantity
A matrix of the estimated heterogeneous quantities
- acov_order
The order of autocovariance
- acor_order
The order of autocovariance
- N
The number of cross-sectional units
- S
The length of time series
- R
The number of bootstrap repetitions
References
Okui, R. and Yanagi, T., 2019. Panel data analysis with heterogeneous dynamics. Journal of Econometrics, 212(2), pp.451-475.
Examples
data <- panelhetero::simulation(N = 300, S = 50)
panelhetero::tojmoment(data = data)
#> $estimate
#> E(mean) E(acov) E(acor) var(mean) var(acov)
#> -0.049192284 0.380922436 0.290531050 1.044624624 0.036145990
#> var(acor) cor(mean, acov) cor(mean, acor) cor(acov, acor)
#> 0.014202369 -0.062391441 -0.009502196 -0.628268583
#>
#> $se
#> E(mean) E(acov) E(acor) var(mean) var(acov)
#> 0.057033428 0.013206558 0.016863231 0.090053800 0.005232293
#> var(acor) cor(mean, acov) cor(mean, acor) cor(acov, acor)
#> 0.007163084 0.061599611 0.089168205 0.088070461
#>
#> $ci
#> 95% CI lower 95% CI upper
#> E(mean) -0.160132502 0.06261817
#> E(acov) 0.356210944 0.40698579
#> E(acor) 0.256536322 0.32335523
#> var(mean) 0.872320535 1.22945946
#> var(acov) 0.026271260 0.04718517
#> var(acor) 0.000170456 0.02823125
#> cor(mean, acov) -0.184663719 0.05585371
#> cor(mean, acor) -0.185812635 0.16909143
#> cor(acov, acor) -0.795892203 -0.44989153
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] -0.213608501 0.12425250 0.198774036
#> [2,] 1.436796065 0.30501662 0.358474097
#> [3,] -1.954641270 0.36150380 0.462529756
#> [4,] -1.375384291 0.18622672 0.277332150
#> [5,] -2.488045524 0.43304986 0.243255104
#> [6,] -0.991085904 0.36644335 0.235078669
#> [7,] 2.265653545 0.16174393 0.001357980
#> [8,] -1.225472469 0.33065011 0.222290442
#> [9,] -1.466507082 0.22169403 0.222794021
#> [10,] 1.224424684 0.74044610 0.376320059
#> [11,] -0.135796161 0.47593738 0.089183023
#> [12,] -0.056068362 0.84731860 0.294657794
#> [13,] 0.137534656 0.19646731 0.634520435
#> [14,] 0.715094755 1.09471023 0.172538500
#> [15,] 1.053044175 0.38464716 0.069372417
#> [16,] -0.921697892 0.52056278 0.283035286
#> [17,] 0.904927589 0.32744356 0.165700559
#> [18,] 0.022839816 0.46566246 0.263724672
#> [19,] -0.326114967 0.51103470 0.227939994
#> [20,] -0.779801348 0.63766400 0.536281916
#> [21,] 1.803304480 0.76555572 0.198884642
#> [22,] -1.331082936 0.18644465 0.145090617
#> [23,] -0.738546788 0.74811895 0.105937655
#> [24,] -0.143052595 0.06211099 0.404488978
#> [25,] 0.905642761 0.20128323 0.523702418
#> [26,] -0.985048860 0.45845330 0.249500371
#> [27,] -1.251393162 0.19420308 0.290391164
#> [28,] 1.403399852 0.22452536 0.254677542
#> [29,] -0.080667804 0.13177745 0.360063132
#> [30,] 0.619239431 0.40832854 0.069820625
#> [31,] -0.724126591 0.23494873 0.161252547
#> [32,] -0.713763520 0.28141933 0.277819190
#> [33,] 0.576587144 0.15002007 0.534850209
#> [34,] -1.137436350 0.41376270 0.023100928
#> [35,] -0.539948315 0.32833322 0.199049392
#> [36,] 0.563224344 0.49305892 0.006473744
#> [37,] 0.032329469 0.44689308 0.364156429
#> [38,] -1.324501085 0.38787915 0.651641326
#> [39,] -0.229753292 0.16572302 0.196602430
#> [40,] 0.059805650 0.22922628 0.430721601
#> [41,] 0.017000867 0.31626659 -0.047316718
#> [42,] 1.982281269 0.58583448 0.201181706
#> [43,] -0.464558219 0.22207451 0.270720834
#> [44,] -1.845952866 0.35052185 0.510398184
#> [45,] 0.590249330 0.51083572 0.281504708
#> [46,] -1.926381583 0.33327119 0.281649488
#> [47,] -1.146701112 0.19668268 0.384013437
#> [48,] -0.211208468 0.56654732 0.492234954
#> [49,] -1.297983040 0.20413779 0.391688389
#> [50,] 0.497053995 0.33971394 0.182697215
#> [51,] 0.382675726 0.25439568 0.314828648
#> [52,] -0.167608133 0.65163144 0.332221318
#> [53,] -0.110914683 0.18901808 0.568984942
#> [54,] 0.190421428 0.09688350 0.668047975
#> [55,] -0.954695377 0.50771964 0.197084219
#> [56,] 0.185822832 0.30812463 0.490122730
#> [57,] 0.030700885 0.23114685 0.630156554
#> [58,] 0.477049812 0.11288559 0.406904204
#> [59,] -1.695441010 0.53739515 0.131163045
#> [60,] 0.356849549 0.18497006 0.343017187
#> [61,] -0.916094675 0.28672305 0.324185765
#> [62,] 0.337861145 0.18952750 0.379914794
#> [63,] -0.626132328 0.22795670 0.472538351
#> [64,] 0.542592809 0.14475955 0.126015546
#> [65,] -0.072980289 0.31001965 -0.134943681
#> [66,] -0.174997606 0.60914089 0.094506752
#> [67,] 1.581463466 0.60879994 0.410086632
#> [68,] -1.251457168 0.31069629 0.167730687
#> [69,] -0.879366845 0.24532670 0.007581016
#> [70,] 0.200837837 1.04214919 0.302963759
#> [71,] -0.086152763 0.74960338 -0.040295211
#> [72,] 0.025077309 0.12437869 0.339369963
#> [73,] -1.561113498 0.25172928 0.153840519
#> [74,] -0.081254891 0.06889043 0.478808322
#> [75,] 0.603693468 0.52782646 0.343024802
#> [76,] 0.607606925 0.35898846 0.159195414
#> [77,] 1.870724360 0.22859328 0.140134894
#> [78,] -1.270942070 0.33473866 0.168612127
#> [79,] 0.516144584 0.57156950 -0.091643750
#> [80,] 0.773516847 0.46517788 0.406526912
#> [81,] 0.506389541 0.39976621 -0.074618165
#> [82,] 0.599686509 0.09753647 0.485239772
#> [83,] -0.668208857 0.88356778 -0.355733285
#> [84,] -1.000022401 0.09881832 0.668749424
#> [85,] 0.275897993 0.14942970 0.611075479
#> [86,] 1.052143150 0.17154764 0.077978544
#> [87,] -2.257458569 0.58444272 0.159413092
#> [88,] -0.273878813 0.60608431 0.098667974
#> [89,] 0.775974098 0.58957002 0.266054708
#> [90,] -0.945906588 0.14972051 0.678646603
#> [91,] -0.056814605 0.25786996 -0.069186514
#> [92,] 1.992039158 0.42009345 0.344601092
#> [93,] -0.373320105 0.40095781 0.323298453
#> [94,] -0.789115926 0.76015035 0.164777273
#> [95,] -0.564988615 0.14599312 0.211911363
#> [96,] 0.225030843 0.19157263 0.202749284
#> [97,] -0.673215027 0.76478291 0.173186069
#> [98,] 0.207537169 0.51972272 0.224720154
#> [99,] -0.346096875 0.08838454 0.249524364
#> [100,] -0.081055657 0.17347548 0.687870324
#> [101,] -0.624372481 0.15825896 0.794355468
#> [102,] 0.089902869 0.95763015 -0.153401322
#> [103,] 1.027288307 0.74360853 0.220488075
#> [104,] -1.508516429 0.16188846 0.232777289
#> [105,] -0.495097298 0.98495206 -0.040817560
#> [106,] -1.577471977 0.20103738 0.282792229
#> [107,] 0.602801706 0.82260899 0.345451089
#> [108,] 1.030650545 0.19042911 0.002578848
#> [109,] -0.851815408 0.70425740 0.234092495
#> [110,] -0.310877180 1.08106386 0.009439485
#> [111,] -1.514075704 0.36663373 -0.027840159
#> [112,] -0.795246461 0.13059292 0.464149530
#> [113,] -1.279199411 0.56905814 -0.016803855
#> [114,] 1.561253984 0.16560760 0.333160777
#> [115,] 0.415123260 0.64614569 0.056122472
#> [116,] -1.272347029 0.19177879 0.180403935
#> [117,] 1.069232570 0.19115610 0.297268808
#> [118,] -1.016959955 0.53141881 0.213588314
#> [119,] 0.244118779 0.24888215 0.456053392
#> [120,] 3.859080062 0.34084221 0.241086340
#> [121,] -0.053645271 0.73399633 0.086635498
#> [122,] 0.607766176 0.12262438 0.239925914
#> [123,] -1.443360286 0.63729889 0.202846699
#> [124,] 0.632207738 1.11755172 -0.076899158
#> [125,] 0.349027911 0.20335649 0.484430701
#> [126,] 0.213272886 0.33747510 0.091054907
#> [127,] 1.251681590 0.15253257 -0.164632779
#> [128,] -0.303222749 0.29130108 0.033432298
#> [129,] 2.427514702 0.38274339 0.552747628
#> [130,] -0.766292372 0.30199242 0.046067627
#> [131,] 0.023290691 0.23678821 0.067640988
#> [132,] -0.664566479 0.68122310 0.374009039
#> [133,] 0.590319469 0.12079593 0.356371639
#> [134,] 0.254782352 0.80201322 0.400699722
#> [135,] -0.002124489 0.37422379 0.177144472
#> [136,] -1.157021359 0.17712479 0.285548703
#> [137,] 0.767792962 0.18673813 0.205872358
#> [138,] 0.566022041 0.32209365 0.218838658
#> [139,] -0.240767059 0.38811109 -0.020427112
#> [140,] 1.238401307 0.20367323 0.370065777
#> [141,] -0.391539665 0.30713071 0.006390556
#> [142,] -0.370088484 0.15811333 0.197428949
#> [143,] -0.199212119 0.43329469 0.301450152
#> [144,] 0.292491155 0.47506751 0.359906368
#> [145,] 1.142555138 0.08273131 0.416250827
#> [146,] 0.757605446 0.49874509 0.105897074
#> [147,] -1.448857343 0.44890019 0.438055337
#> [148,] -0.754833103 0.32687847 0.244856569
#> [149,] -1.764480100 0.38859318 0.185971130
#> [150,] -0.560362188 0.88453645 -0.122155393
#> [151,] 2.084735484 0.19166553 0.575504619
#> [152,] 0.177252569 0.50489452 0.143823616
#> [153,] -0.267501297 0.28308295 0.132591070
#> [154,] 1.194903572 0.13302122 0.269915436
#> [155,] -0.848709885 0.17401572 0.234265008
#> [156,] -1.664761084 0.97509369 0.247392609
#> [157,] -0.561565075 0.32133287 0.294757277
#> [158,] 0.710980588 0.55468949 0.140037682
#> [159,] 0.841754794 0.18136885 0.181702145
#> [160,] 1.408765150 0.46037027 0.363481406
#> [161,] 0.342151061 0.18108982 0.097924567
#> [162,] 0.053434212 0.48810318 0.226976965
#> [163,] -0.682500740 0.57253996 0.051351856
#> [164,] 0.533656103 0.21245504 0.005928281
#> [165,] 0.923249163 0.47472594 0.416109074
#> [166,] 0.849787430 0.61567337 0.435990740
#> [167,] 0.792961805 0.13485238 0.557242547
#> [168,] 0.197509068 0.44017563 0.200384228
#> [169,] 1.961833291 0.49401208 0.543501446
#> [170,] 0.248500553 0.29087181 0.276501516
#> [171,] -0.516804218 0.27243611 0.086177832
#> [172,] -0.313884751 0.26916384 0.341434352
#> [173,] -0.940627040 0.49330351 0.311698491
#> [174,] 1.091695000 0.63575643 0.024084030
#> [175,] -1.632301345 0.41547739 0.274845184
#> [176,] 0.290282826 0.21100348 0.250955714
#> [177,] -0.875494495 0.28560222 -0.014972039
#> [178,] -0.149048343 0.87036765 0.059136687
#> [179,] 1.657610438 0.09456416 0.475440019
#> [180,] 0.355687181 0.11442459 0.643961350
#> [181,] -1.184461580 0.30901217 0.160519534
#> [182,] 0.055604259 0.15876472 0.487690187
#> [183,] 1.026142580 0.30894139 0.116440594
#> [184,] 1.647700739 0.52275897 0.168744225
#> [185,] -0.402013318 0.42798749 0.126111000
#> [186,] 0.195131752 0.39599775 0.152578769
#> [187,] -0.778825102 0.53303454 0.351271082
#> [188,] -0.269272472 0.16015388 0.525112071
#> [189,] -1.082697213 0.45109206 0.122725294
#> [190,] 1.367199504 0.17877936 0.590591389
#> [191,] 1.131446325 0.41987218 0.323736355
#> [192,] 0.149156099 0.39970709 0.020601898
#> [193,] 0.529159725 0.44289883 0.196790961
#> [194,] -0.040768134 0.44197647 0.065957636
#> [195,] -0.390192872 0.37267392 0.365742843
#> [196,] 1.333558719 0.13228707 0.619590211
#> [197,] -0.782652610 0.27924727 -0.110960483
#> [198,] -0.859345141 0.38471365 0.462781155
#> [199,] 1.736415276 0.25018242 0.299371333
#> [200,] 0.330707561 0.13875223 0.474856158
#> [201,] -0.577451964 0.41178337 0.408446980
#> [202,] -0.022688798 0.95747367 0.260524329
#> [203,] -1.960979630 0.86453300 -0.185387398
#> [204,] -1.794191160 0.66328806 0.248056342
#> [205,] 0.188920574 0.88944032 0.172790145
#> [206,] -2.375478136 0.15272703 0.231174231
#> [207,] 0.331780983 0.28156174 0.183572245
#> [208,] 1.532001986 0.29043073 -0.040289219
#> [209,] -0.078525116 0.13791736 0.256088574
#> [210,] -0.042812534 0.25200209 0.123353553
#> [211,] 0.598525913 0.11385187 0.449401358
#> [212,] -0.599218393 0.20449928 0.380453840
#> [213,] -1.333651884 0.36365018 0.076571798
#> [214,] -0.516557022 0.18966218 0.208762476
#> [215,] -1.647181289 0.55866737 0.515593931
#> [216,] -0.658507080 0.22524773 0.258948398
#> [217,] 0.558753938 0.30325507 -0.006210116
#> [218,] -0.530675159 0.25615492 0.352766530
#> [219,] -1.547376929 0.19577427 0.290876657
#> [220,] -1.618753583 0.50624532 0.542378372
#> [221,] 1.652066347 0.70763369 -0.113684075
#> [222,] 0.229780783 0.11404423 0.770543926
#> [223,] -0.976998633 0.33117014 0.413884015
#> [224,] 0.199620949 0.23522260 -0.185298070
#> [225,] -0.028602806 0.55933703 -0.063080089
#> [226,] -0.668026969 0.32342404 0.076533466
#> [227,] -1.075435188 0.26765442 0.602857446
#> [228,] 0.593110597 0.34997458 0.211517651
#> [229,] 1.057252709 0.13209799 0.262648421
#> [230,] -0.648754898 0.08449352 0.335251249
#> [231,] -0.035286557 0.38692800 0.286090544
#> [232,] 0.123561190 0.28842612 0.316305719
#> [233,] 1.280296454 0.12888855 0.526365197
#> [234,] -0.732970674 0.37077902 0.441458240
#> [235,] -0.518432509 0.21713778 0.241421746
#> [236,] -0.054565582 0.44428083 0.374884174
#> [237,] 1.025094676 0.14044131 0.233862651
#> [238,] -0.805879414 0.58960716 0.462067321
#> [239,] 2.074504663 0.10524818 0.404611420
#> [240,] -0.875002094 0.39106815 0.101670076
#> [241,] -1.266782620 0.63948876 0.081367673
#> [242,] -0.260155489 0.34533840 0.249172398
#> [243,] 0.038034833 0.44879752 0.335911125
#> [244,] -0.231705386 0.42028807 0.002271494
#> [245,] 0.419365532 0.34524091 0.720711661
#> [246,] 1.015185653 0.40009161 -0.056161437
#> [247,] 1.341930970 0.23292642 0.299155642
#> [248,] -1.143742166 0.16416153 0.005707448
#> [249,] -2.487659921 0.38391307 0.214685192
#> [250,] 1.061081682 0.66308028 0.165308276
#> [251,] -1.611011829 0.49317562 0.437574544
#> [252,] 1.759256053 0.46720877 -0.005523462
#> [253,] -2.142420070 0.21513487 0.168326218
#> [254,] -0.681221460 0.35809420 0.246762496
#> [255,] -0.969323690 0.31633419 0.024290389
#> [256,] 0.747291635 0.21831710 -0.072052440
#> [257,] 2.286075721 0.56226382 0.436433411
#> [258,] -0.209305975 0.40809332 0.254304133
#> [259,] -0.467449626 0.37591323 -0.155927526
#> [260,] -0.709511834 0.15594628 0.353373635
#> [261,] -1.633951704 0.85536425 0.051912685
#> [262,] -0.159453157 0.33005236 0.133663055
#> [263,] -0.589173191 0.46976381 0.307622249
#> [264,] -2.229117250 0.40301200 0.531863307
#> [265,] 0.149127647 0.20848267 0.211275280
#> [266,] 2.678860453 0.62579966 0.063730581
#> [267,] -0.616148539 0.19140780 0.721708863
#> [268,] -0.576182496 0.10928557 0.462787329
#> [269,] 0.201677716 0.56344701 0.034574983
#> [270,] -1.418394871 0.26139907 0.550793644
#> [271,] -0.747506216 0.08344598 0.551543042
#> [272,] 1.301977650 0.39304636 0.114175718
#> [273,] -0.022718621 0.17637147 -0.139247685
#> [274,] -0.042943981 0.33945682 0.463060361
#> [275,] 0.086120738 0.22567807 0.383097307
#> [276,] 2.122679753 0.34848126 0.261697060
#> [277,] 0.213831475 0.35254659 0.154755463
#> [278,] -0.071937038 0.53100479 0.152522619
#> [279,] 0.526000175 0.23742428 0.031503018
#> [280,] 1.227055414 0.56841082 0.387413208
#> [281,] 0.676268292 0.56954795 0.154448950
#> [282,] -0.269656266 0.43448678 0.302777067
#> [283,] -1.504221752 0.09844186 0.258158277
#> [284,] 0.370985097 0.52826014 0.137926239
#> [285,] 0.508810190 0.56672151 0.119358231
#> [286,] -1.176381436 0.36096677 0.104305351
#> [287,] -0.423072260 0.23050482 0.484201045
#> [288,] 1.097346573 0.14402093 0.245494295
#> [289,] 0.175698446 0.45193791 -0.052613907
#> [290,] 1.119665430 0.14391526 0.647382102
#> [291,] 0.701372797 0.26509049 0.100830725
#> [292,] 0.618090185 0.29442852 0.479863023
#> [293,] -1.295403111 0.22071879 0.034998363
#> [294,] 0.066576995 0.35410953 -0.159708601
#> [295,] 1.012707570 0.29694148 0.358829087
#> [296,] -0.926596793 0.07931723 0.256243447
#> [297,] 0.740981448 0.17797805 0.280022973
#> [298,] 0.324627610 0.29501512 0.520477763
#> [299,] 0.533896465 0.18407882 0.434900503
#> [300,] 0.441001437 0.64930083 0.325124390
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>
#> $R
#> [1] 1000
#>