The HPJ bias-corrected estimation of the moments
hpjmoment.RdThe `hpjmoment()` function enables to implement the HPJ 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::hpjmoment(data = data)
#> $estimate
#> E(mean) E(acov) E(acor) var(mean) var(acov)
#> 0.09940194 0.36926029 0.28092487 1.09583883 0.03500338
#> var(acor) cor(mean, acov) cor(mean, acor) cor(acov, acor)
#> 0.01856102 0.07564245 0.03085462 -0.41747452
#>
#> $se
#> E(mean) E(acov) E(acor) var(mean) var(acov)
#> 0.059396378 0.011754966 0.011987997 0.085545685 0.004415153
#> var(acor) cor(mean, acov) cor(mean, acor) cor(acov, acor)
#> 0.003760836 0.056121769 0.072475245 0.061398448
#>
#> $ci
#> 95% CI lower 95% CI upper
#> E(mean) -0.01721770 0.2216830
#> E(acov) 0.34746933 0.3922490
#> E(acor) 0.25867967 0.3049867
#> var(mean) 0.92432404 1.2597706
#> var(acov) 0.02718950 0.0447497
#> var(acor) 0.01113975 0.0259475
#> cor(mean, acov) -0.03195630 0.1907651
#> cor(mean, acor) -0.10405633 0.1695519
#> cor(acov, acor) -0.54112082 -0.2963990
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] -1.26522148 0.36623478 0.069213608
#> [2,] 0.73517956 0.51642541 -0.105782063
#> [3,] -0.29687625 0.39777877 0.281125879
#> [4,] -0.15930530 0.28011801 0.077102282
#> [5,] -0.68627542 0.28757180 0.027208232
#> [6,] -1.24720952 0.19070506 0.347300680
#> [7,] 0.93409498 0.18368257 0.750339508
#> [8,] 0.25368147 0.36739619 0.263348856
#> [9,] 1.35727911 0.64982226 0.380282184
#> [10,] -0.36255001 0.10248726 0.345142763
#> [11,] 1.20121492 0.15856813 0.138360732
#> [12,] 0.20815140 0.48313688 0.364511232
#> [13,] -1.21137275 0.34608162 0.081889193
#> [14,] 0.86491029 0.79380223 -0.050573966
#> [15,] -0.44471806 0.23357343 0.524160556
#> [16,] 1.86939274 0.25200454 0.330000544
#> [17,] 1.55385602 0.23787968 0.240115125
#> [18,] -0.27070921 0.40665790 0.456580007
#> [19,] -1.36707854 0.24389098 0.463343247
#> [20,] -0.01154721 0.35226795 0.489949510
#> [21,] 0.46420104 0.55290665 0.208461611
#> [22,] 2.03977858 0.39787896 0.121700035
#> [23,] -0.38495479 0.40474565 -0.086368151
#> [24,] -0.18911315 0.09464281 0.178704952
#> [25,] 1.54072567 0.47006387 0.079698060
#> [26,] 0.41780466 0.75782993 0.376418752
#> [27,] 0.38502850 0.26771253 0.322365371
#> [28,] -0.77396473 0.45846254 0.066613882
#> [29,] -0.36866216 0.22930317 0.289762175
#> [30,] 1.23586941 0.87604446 0.178226268
#> [31,] 1.26038365 0.18709155 0.437489382
#> [32,] -1.09998481 0.58899851 -0.129650334
#> [33,] -0.44074781 0.23829233 0.411012207
#> [34,] -0.52000154 0.16917626 0.254423344
#> [35,] -0.50925893 0.56176506 0.147656055
#> [36,] 0.50932078 0.31344534 0.250446968
#> [37,] -0.16023782 0.61054399 0.269531598
#> [38,] 0.61087025 0.51684292 0.202322103
#> [39,] -1.55138864 0.43373837 0.383183074
#> [40,] -0.38190418 0.53947554 0.083673900
#> [41,] 1.63577818 0.19335780 0.422074503
#> [42,] 0.99574317 0.25942092 0.004163398
#> [43,] 0.64266352 0.30423101 0.065167352
#> [44,] 0.50228930 0.18635048 0.288447257
#> [45,] -0.98294524 0.35330408 0.066990924
#> [46,] 0.76995439 0.34309695 -0.051600309
#> [47,] 1.04186303 0.45863699 0.123575204
#> [48,] 1.04762491 0.18366165 0.297361113
#> [49,] -1.53695316 0.31041354 0.197515977
#> [50,] -0.85657668 0.22026776 0.222212031
#> [51,] -0.35346046 0.61062905 0.341494229
#> [52,] 0.89052141 0.19775084 0.171070578
#> [53,] -0.19952902 0.30751935 -0.016602313
#> [54,] -1.01215849 0.18332656 0.276062862
#> [55,] -0.21294002 0.32671530 0.349353085
#> [56,] -0.63612345 0.50168879 -0.019686644
#> [57,] 1.19565862 0.36778317 0.011880729
#> [58,] 1.74822225 0.23824197 0.233527669
#> [59,] -0.33266394 0.47701286 -0.097680976
#> [60,] 1.49230232 0.61318884 0.136384288
#> [61,] 0.53707698 0.15065805 0.310126534
#> [62,] 0.89541611 0.58335517 0.404618788
#> [63,] -0.34178850 0.27250513 0.205517292
#> [64,] -0.27186560 0.13691871 0.295948727
#> [65,] 0.76618785 0.59253669 0.209919156
#> [66,] -0.67108633 0.11727797 0.343475601
#> [67,] 0.28411504 0.34206369 0.511164642
#> [68,] 1.40450072 0.28474386 0.577761128
#> [69,] 0.76804116 1.04020342 -0.055449973
#> [70,] -1.35774531 0.71174974 0.330993600
#> [71,] -2.26241735 0.27277609 0.320346078
#> [72,] 0.16121322 0.77098013 0.282299749
#> [73,] -0.74191640 0.21448947 0.083028262
#> [74,] 0.38728305 0.30756410 -0.004035052
#> [75,] 1.25527586 1.00286361 0.148130754
#> [76,] 2.70945330 0.14023465 0.316723487
#> [77,] 0.13811545 0.34310877 0.090164521
#> [78,] -1.04615647 0.20014230 0.030783734
#> [79,] -0.25652598 0.48272564 0.053007061
#> [80,] -0.44652863 0.65057468 0.132897342
#> [81,] -2.29833992 0.36976717 0.547502065
#> [82,] 0.32681503 0.20915995 0.669834910
#> [83,] -0.44572230 0.39409866 0.464502413
#> [84,] -2.01062086 0.48947154 0.370855233
#> [85,] 0.40281277 0.69907147 0.036609984
#> [86,] 0.29425599 0.39219392 0.498450797
#> [87,] 0.98107865 0.12976914 0.514174460
#> [88,] 0.73238098 0.42806868 0.186018240
#> [89,] -0.93732584 0.08960648 0.160589480
#> [90,] 2.44207754 0.26331297 0.300260372
#> [91,] 0.09442029 0.28567987 0.368070631
#> [92,] 0.21053658 0.15870822 0.548610327
#> [93,] 2.08943317 0.34789305 0.183229685
#> [94,] 0.11185190 0.20645928 0.619576193
#> [95,] 1.24299013 0.07872115 0.468516248
#> [96,] -0.24692901 0.30729492 -0.020567652
#> [97,] -1.74994138 0.40338360 0.408227968
#> [98,] -2.24255863 0.19782613 0.304851149
#> [99,] 0.82284811 0.75890360 0.072174709
#> [100,] -0.66145411 0.25511353 0.047032329
#> [101,] -0.32615812 0.23552083 0.152281022
#> [102,] -0.51250841 0.10475092 0.368757227
#> [103,] -0.53376199 0.57489036 0.117458772
#> [104,] 0.63006291 0.99211102 0.067785947
#> [105,] 1.06213160 0.81259079 0.148753123
#> [106,] 1.12226133 0.17950382 -0.046667237
#> [107,] -0.24335748 0.20974329 -0.154660277
#> [108,] -1.64423370 0.25110663 0.258425732
#> [109,] -0.90410250 0.26664443 0.178588474
#> [110,] -0.17664184 0.13886637 0.313454351
#> [111,] 0.29726036 0.33895802 0.193889108
#> [112,] 1.52072063 0.56531521 0.073792227
#> [113,] -1.37847326 0.19783709 0.491715893
#> [114,] 1.10367425 0.38096730 0.037232375
#> [115,] 0.82072224 0.36102815 0.292491514
#> [116,] 1.14985783 0.11094976 0.038684485
#> [117,] -0.56351473 0.18911625 0.077765677
#> [118,] 0.48900454 0.11831585 0.274471035
#> [119,] 0.12739861 0.49678603 0.423960981
#> [120,] 1.02112906 0.30691615 0.368161532
#> [121,] -1.02469086 0.35442278 0.099080936
#> [122,] -2.34044126 0.27664068 0.542758570
#> [123,] -0.34658938 0.37893581 -0.146303245
#> [124,] 0.79792904 0.11253942 -0.074412776
#> [125,] 0.73450125 0.35690129 0.260700378
#> [126,] 1.30101967 0.24671762 0.105801640
#> [127,] 0.28762995 0.24244253 0.268321697
#> [128,] 0.93258042 0.54385915 0.215470215
#> [129,] -1.21939832 0.46293782 0.033935811
#> [130,] 0.51744190 0.61181759 0.321915864
#> [131,] -0.06900245 0.18814591 0.248903954
#> [132,] 0.27798411 0.49264959 0.150214021
#> [133,] 0.09407573 0.14000876 0.197676063
#> [134,] -0.91845804 0.47415096 0.317010289
#> [135,] 1.87490761 0.05704506 0.622795375
#> [136,] -1.14612779 0.34725075 -0.237455682
#> [137,] -0.56702103 0.13938875 0.260775112
#> [138,] 0.44542350 0.34265608 -0.096082060
#> [139,] 0.66529168 0.16891783 0.148691536
#> [140,] -0.85230505 0.16307008 -0.010386027
#> [141,] 0.07660187 0.12583364 0.564244608
#> [142,] -0.98690759 0.27692967 0.394062741
#> [143,] 0.89572496 0.45072293 0.498728588
#> [144,] 0.32524386 0.24505937 0.722034246
#> [145,] 0.15920694 0.69989608 0.307449639
#> [146,] -2.17671341 0.58715623 0.008274470
#> [147,] -1.41730080 0.25868418 0.315329969
#> [148,] 1.65787025 0.54072529 0.253183439
#> [149,] 1.29465021 0.29882188 0.528778876
#> [150,] -1.15963884 0.15586888 0.386407172
#> [151,] 1.57764518 0.78235878 0.195213221
#> [152,] 1.59153659 0.16051718 0.425244056
#> [153,] -1.27069647 0.31975038 -0.083730875
#> [154,] 2.16797223 0.38610437 0.542645185
#> [155,] -0.54483047 0.13156530 0.565621095
#> [156,] 0.01933745 0.40167307 0.210326423
#> [157,] -0.56956870 0.68181365 0.113684440
#> [158,] 2.02006885 0.69106008 -0.063623655
#> [159,] 1.50638467 0.33327505 0.073381239
#> [160,] 0.91669044 0.13981567 0.262751916
#> [161,] 3.08209356 0.23172848 0.513965201
#> [162,] 0.31260485 0.46543625 0.096949769
#> [163,] 0.06718945 0.51195898 0.294250540
#> [164,] 2.11360230 0.12634331 0.642841247
#> [165,] -0.66006042 0.32494408 0.351960006
#> [166,] 0.10173961 0.43409472 0.214062028
#> [167,] 2.13507921 0.43691286 0.272539784
#> [168,] -1.39769310 0.44469771 0.195930681
#> [169,] 1.17493713 0.15998715 0.112442503
#> [170,] 1.66326721 0.22239589 0.135802633
#> [171,] 1.48491827 0.37343324 0.414178118
#> [172,] -0.06389913 0.55354190 0.241303961
#> [173,] -0.77952617 0.47735772 0.260395988
#> [174,] -1.76347638 0.28270594 -0.058289507
#> [175,] -0.43757601 0.13943322 0.236444049
#> [176,] -0.35308217 0.09679629 0.328146672
#> [177,] 1.94335683 0.42334395 0.131623070
#> [178,] -0.99912264 0.29498502 0.318557705
#> [179,] -0.27766710 0.36696006 0.163550351
#> [180,] 0.70854845 0.05315931 0.340206103
#> [181,] 0.07663444 0.57414109 0.050369983
#> [182,] 0.92640703 0.35630600 0.021158211
#> [183,] 0.33090541 0.35695006 0.240001092
#> [184,] -0.40719696 0.47424335 0.387886647
#> [185,] 1.37398826 0.12241154 0.844438885
#> [186,] -1.36822159 0.18049069 0.198540258
#> [187,] 0.14945146 0.19601638 0.280146451
#> [188,] -1.69889881 0.22558392 -0.037430646
#> [189,] -1.03729673 0.37202206 0.049993511
#> [190,] 1.05495846 0.44169439 0.265422142
#> [191,] 0.76479510 0.39670710 0.122211819
#> [192,] 0.59765173 0.15447682 0.375545033
#> [193,] -0.25889009 0.19156714 0.437389852
#> [194,] 2.04714011 0.35160929 0.464415206
#> [195,] -0.53446941 0.22123538 0.384296534
#> [196,] 0.72457435 0.64547954 0.199619207
#> [197,] -1.75506639 0.12771338 0.157840972
#> [198,] -0.34617679 0.26196154 -0.145188390
#> [199,] -0.01233208 0.52256726 0.076140718
#> [200,] 0.70803098 0.47825680 0.342152230
#> [201,] 0.07980638 0.24188381 0.152751844
#> [202,] -0.45666289 0.42253939 0.239539418
#> [203,] -0.66042774 0.51472137 0.213676011
#> [204,] 0.22463101 0.31237333 0.490637422
#> [205,] 1.50398476 0.08805337 0.318865320
#> [206,] -0.93059348 0.28288775 0.396223163
#> [207,] 0.08960821 0.76183385 0.286566686
#> [208,] -0.50161791 0.23419635 0.448808323
#> [209,] -1.03453697 0.46116708 -0.091912120
#> [210,] 0.79646738 0.36600274 0.134036048
#> [211,] -1.43578378 0.53064476 0.644387761
#> [212,] -0.23315572 0.67170416 -0.070862671
#> [213,] 2.60074547 0.53226854 0.053371951
#> [214,] -1.85362736 0.13756753 0.491498956
#> [215,] -0.12778573 0.32461228 0.484140252
#> [216,] -0.71973397 0.42885017 0.538885077
#> [217,] 0.63404499 0.26195997 0.221983699
#> [218,] 1.16693598 0.22217062 0.464067866
#> [219,] -0.78965489 0.60689900 0.516048593
#> [220,] -0.98955868 0.32652857 0.004353589
#> [221,] 0.34758129 1.18266918 0.390996789
#> [222,] -1.82869558 0.53895367 0.050181971
#> [223,] 0.46729606 0.31059962 -0.030363833
#> [224,] -0.33365857 0.18334852 0.142167115
#> [225,] -0.03758142 0.21974264 0.419759835
#> [226,] -2.05799434 0.20185056 0.293906398
#> [227,] -1.14342640 0.60072031 -0.007181979
#> [228,] -0.54020612 0.36959552 0.245511394
#> [229,] -1.12765605 0.31998066 0.309664664
#> [230,] 0.54326657 0.20436812 0.174175977
#> [231,] 0.19485907 0.36196295 0.027507836
#> [232,] -0.52767383 0.30618330 0.262171543
#> [233,] -0.50213441 0.54687533 0.130675622
#> [234,] -1.14419669 0.44294999 0.182403711
#> [235,] 0.14793629 0.38367074 0.134581538
#> [236,] 0.13742070 0.18943444 0.615586936
#> [237,] 1.73329421 0.35304611 0.119330759
#> [238,] 0.28091951 0.19213866 0.145063853
#> [239,] 1.06592479 0.22144970 0.476277480
#> [240,] 0.55216367 0.48690699 0.336625122
#> [241,] -0.50568330 0.69990359 0.147133500
#> [242,] -0.15888848 0.57065297 0.032227789
#> [243,] 1.11129395 0.47685209 0.309205299
#> [244,] -0.17180811 0.58338577 -0.026783065
#> [245,] 0.77229859 0.39820027 0.046696092
#> [246,] 0.64388907 0.11664938 0.400841674
#> [247,] -0.57132147 0.20769281 0.436237589
#> [248,] -0.50697388 0.24114828 0.461461274
#> [249,] -1.46022126 0.21572637 0.187962547
#> [250,] -0.56083381 0.14584238 0.056804254
#> [251,] -0.68802760 0.25389621 0.429107580
#> [252,] -0.11276842 0.28184464 0.143069278
#> [253,] 1.70707805 0.27598790 -0.004624171
#> [254,] 0.13519387 0.57224970 -0.052841855
#> [255,] 1.10359068 0.04708678 0.406214025
#> [256,] -0.81044768 0.33746308 0.136106812
#> [257,] 0.97782241 0.47783851 0.370151758
#> [258,] -1.44796864 0.22984448 0.311967504
#> [259,] 0.94861055 0.76793857 -0.025159593
#> [260,] -0.80699030 0.29761295 0.260206402
#> [261,] 0.88160992 0.12492064 0.147905791
#> [262,] -0.20397844 0.21779915 0.008367611
#> [263,] 0.72994345 0.57438068 0.195454605
#> [264,] 0.38035610 0.74340262 0.431520556
#> [265,] 0.63856854 0.10907809 0.523392131
#> [266,] -1.34269377 0.13057659 0.468290503
#> [267,] 0.82864834 0.22244374 0.419033377
#> [268,] -1.02036619 0.29230320 0.317756791
#> [269,] 0.26684293 0.27470618 0.508526925
#> [270,] -0.28595694 0.58657372 0.118640659
#> [271,] -0.91578055 0.12706369 0.331257170
#> [272,] 0.76218475 0.39792072 0.053743254
#> [273,] 1.22151307 0.22059646 0.231100564
#> [274,] 0.47907685 0.99484364 0.160558852
#> [275,] -0.40512906 0.67039856 0.302245936
#> [276,] 2.29695149 0.07764267 0.381344173
#> [277,] 1.25024155 0.35283474 0.171915225
#> [278,] 1.32161545 0.89220899 0.150967723
#> [279,] 0.44388302 0.78856520 0.184843035
#> [280,] -0.08421231 0.35920913 0.255710539
#> [281,] -0.80291658 0.07287374 0.436977787
#> [282,] -1.99151755 0.25055744 0.362867876
#> [283,] 2.35625372 0.13755766 0.136097395
#> [284,] -0.29152228 0.39391821 0.548264498
#> [285,] 1.33950519 0.22339981 0.272118139
#> [286,] -1.12820755 0.35990021 0.298955894
#> [287,] 1.28316994 0.32570703 0.295621441
#> [288,] -1.45560352 0.21128106 0.612762390
#> [289,] 0.93928914 0.74289231 0.061262825
#> [290,] -0.50812360 0.14717881 0.704592476
#> [291,] 0.85955550 0.19943879 0.394496411
#> [292,] 0.15305484 0.15302870 0.327474961
#> [293,] 1.06545534 0.16575894 0.331373268
#> [294,] 0.13813037 0.21630102 0.576794828
#> [295,] 0.26752289 0.26782212 -0.071215673
#> [296,] -0.50887221 0.30858670 0.143404835
#> [297,] 0.95425501 0.45043152 0.038533487
#> [298,] -0.21396934 0.10824036 0.159173253
#> [299,] -1.38646242 0.25415870 0.286547421
#> [300,] -0.30801266 0.57091704 0.236288948
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>
#> $R
#> [1] 1000
#>