Hello, I'm new in the forum and have a question for you.
I work with panel data coming from a research network. The underlying firm-level raw data of each member country is confidential. Therefore and for reasons of comparability, the data is pooled and aggregated at different sector levels. However, the data set available to me does not only contain the respective mean values, but all values of the underlying distribution created during the aggregation.
In order to show as part of my analysis how the distribution of a variable has changed over time per sector or country, I would like to present it graphically.
Since I have all relevant properties of the distribution per country/year/sector as own variables, I am looking for a way to calculate different kernels by interpolating the available moments of the distribution.
I am in the field of kernel density estimation, but due to the unusual approach I lack the idea for a further approach.
I know I could plot the 10th and 90th percentile over time, but a typical view of a distribution would be more appropriate.
I hope I have created a good data example and am looking forward to your suggestions.
Data example:
Info:
variable_p1 = value at 1st percentile, variable_p10 = value ar 10st percentile,
variable_sd = standard deviation,
variable_skew = skewness
variable_iqr = interquartile range.
I work with panel data coming from a research network. The underlying firm-level raw data of each member country is confidential. Therefore and for reasons of comparability, the data is pooled and aggregated at different sector levels. However, the data set available to me does not only contain the respective mean values, but all values of the underlying distribution created during the aggregation.
In order to show as part of my analysis how the distribution of a variable has changed over time per sector or country, I would like to present it graphically.
Since I have all relevant properties of the distribution per country/year/sector as own variables, I am looking for a way to calculate different kernels by interpolating the available moments of the distribution.
I am in the field of kernel density estimation, but due to the unusual approach I lack the idea for a further approach.
I know I could plot the 10th and 90th percentile over time, but a typical view of a distribution would be more appropriate.
I hope I have created a good data example and am looking forward to your suggestions.
Data example:
Info:
variable_p1 = value at 1st percentile, variable_p10 = value ar 10st percentile,
variable_sd = standard deviation,
variable_skew = skewness
variable_iqr = interquartile range.
Code:
input str13 country byte sector int year float(variable_iqr variable_mean variable_p1 variable_p10 variable_p20 variable_p30 variable_p40 variable_p50 variable_p60 variable_p70 variable_p80 variable_p90 variable_p99 variable_sd variable_skew) "country1" 1 2002 .08316796 .04337303 -.2269545 -.0532232 -.011277346 .010716712 .02375466 .03676545 .05130272 .07306185 .100204 .15511613 .3231776 .09509224 .10951895 "country1" 1 2003 .08760485 .04784622 -.238902 -.05387203 -.006918778 .012898994 .026654657 .04035446 .055961 .0764264 .11114395 .16308586 .3396377 .09903994 -.1742165 "country1" 1 2004 .09420463 .05783209 -.2124942 -.04086492 .00027718392 .01729789 .031905305 .04634453 .06357674 .08829361 .12173408 .18030873 .3410014 .0994368 .2256225 "country1" 1 2005 .09012224 .05646351 -.20423368 -.03779425 -.0001217368 .01812411 .03113085 .0444632 .05982694 .0839219 .11683664 .1784417 .3368082 .09902152 .18024056 "country1" 1 2006 .09225135 .06384529 -.20904528 -.029345926 .005902195 .022295317 .036943417 .05125748 .06885449 .09295981 .12435046 .1867929 .3494133 .10115737 .08973073 "country1" 1 2007 .0944089 .07030966 -.200514 -.02299091 .01086669 .02682073 .04079077 .05686638 .0752304 .09839115 .13225667 .19800973 .3731743 .10323163 .1156162 "country1" 1 2008 .08910593 .05157742 -.21418253 -.0472291 -.0039400365 .014217508 .02860503 .04301681 .05936781 .08179826 .11261054 .1664505 .3475431 .10136232 .017438319 "country1" 1 2009 .08879016 .03437477 -.29379678 -.08138897 -.023671916 .004407109 .02002304 .033010032 .04734708 .0693822 .10187984 .1594217 .3151034 .10845645 -.4760354 "country1" 1 2010 .0844996 .04771335 -.24874413 -.05143419 -.003691586 .013759927 .025977327 .0409242 .05654737 .0774783 .10947449 .16915904 .3276501 .1016138 -.16067374 "country1" 1 2011 .08636101 .04614235 -.2490693 -.05100594 -.005127077 .012980284 .025043065 .03815276 .05374928 .0765989 .1099275 .16314936 .3277772 .10166649 -.6308886 "country1" 1 2012 .08054356 .03675485 -.28166053 -.06294364 -.013115568 .008894721 .02022787 .03260161 .04678672 .06719011 .09600998 .14604461 .3096482 .10228572 -.8992358 "country1" 1 2013 .08239385 .03785191 -.2814472 -.06107039 -.010723745 .00920183 .021132715 .033136528 .04934089 .070009016 .10093711 .1498375 .3013457 .10366511 -1.341187 "country1" 2 2002 .0627019 .04205047 -.21945067 -.02454038 .0022463268 .015738012 .027031057 .037169337 .04849279 .06162702 .08641662 .13134596 .28052965 .07667319 -.16070695 "country1" 2 2003 .06768013 .04924818 -.15363346 -.018322797 .006698778 .01925186 .029402364 .03931371 .05147231 .06820378 .09342184 .13676676 .2991673 .0759141 .3789564 "country1" 2 2004 .07669906 .05618588 -.17210683 -.021223376 .008581352 .02094011 .031564146 .04406964 .05790789 .07693617 .10467806 .15257367 .32345095 .0832039 .5413909 "country1" 2 2005 .07938947 .0593927 -.15541866 -.014345991 .009026434 .021831963 .033671267 .04741229 .06235425 .08438019 .11383524 .162495 .3179156 .08249186 .51414 "country1" 2 2006 .08062854 .06692433 -.1634248 -.007388396 .01581779 .02819534 .04043319 .05365132 .069686465 .0892066 .11928416 .1741597 .3126176 .08454597 .528312 "country1" 2 2007 .09292187 .07860535 -.12440933 .0007235563 .01909636 .032941516 .04591584 .06205329 .07874315 .10215499 .13848025 .19510522 .3539599 .08743784 .7980635 "country1" 2 2008 .08772802 .06958125 -.1865783 -.008987294 .017663434 .0319069 .04312719 .05589181 .074084274 .09711093 .13075656 .1784043 .3147029 .08887393 .1916717 "country1" 2 2009 .0889101 .06163063 -.1977266 -.02440864 .011642433 .023244144 .035444267 .04906999 .066813014 .09074421 .12116195 .1783725 .3230658 .09310164 .10526872 "country1" 2 2010 .08982925 .06084604 -.21244177 -.024445 .0070021 .02130875 .03324448 .0470635 .06268345 .0862064 .12098616 .17573553 .3419302 .09353782 .4644793 "country1" 2 2011 .076959 .06246951 -.18848687 -.014638877 .013150398 .02579413 .035470698 .04758143 .06011051 .08371626 .11570573 .16803536 .3714702 .09028005 .640537 "country1" 2 2012 .0804705 .05511247 -.2059107 -.02659491 .005919102 .020455085 .032167558 .04330483 .0579785 .07891664 .11019504 .1662839 .327923 .08979089 .22075145 "country1" 2 2013 .07554326 .05154622 -.1689675 -.03370087 .00490463 .016947856 .02757569 .0387764 .05649577 .07565322 .10286155 .1515765 .3350163 .08709578 .53367597 "country1" 3 2003 .09122849 .06262818 -.24306075 -.029420825 .0040391153 .020477816 .03497442 .04903678 .06679774 .0896233 .1249305 .18992163 .3666023 .10096576 .28096178 "country1" 3 2004 .10078674 .07252583 -.25016567 -.02256427 .010115304 .02655589 .04055826 .05832082 .07551766 .1041439 .14055352 .20828202 .3658466 .10598885 .1510424 "country1" 3 2005 .09898855 .07094148 -.2065635 -.024892705 .00942316 .025966566 .04005685 .05577689 .07391926 .0998694 .13980938 .20363896 .3806957 .10238758 .4343913 "country1" 3 2006 .10291824 .07835442 -.1961883 -.01611834 .014111687 .03071813 .04509662 .06032554 .08240695 .10994664 .1477315 .2053013 .4150353 .1034448 .51013935 "country1" 3 2007 .10522886 .08325966 -.1678477 -.00976805 .016769616 .033359308 .04827565 .065436356 .08835565 .11481205 .1506843 .2136377 .3911152 .10064045 .6011094 "country1" 3 2008 .09703624 .06579248 -.2225323 -.02544917 .005734273 .023424465 .03765804 .05235993 .070648946 .0961218 .13066387 .1872563 .3659742 .100927 .0264542 "country1" 3 2009 .0913311 .06082537 -.20352305 -.032934334 .003458004 .01892804 .033576917 .04834393 .06575807 .08977359 .12545522 .1827074 .3554281 .09734005 .3680397 "country1" 3 2010 .09285816 .06818405 -.1732493 -.018079871 .010569886 .02504931 .03881498 .05368638 .07305725 .09603573 .12871188 .18236166 .3662269 .09531443 .4595095 "country1" 3 2011 .08910906 .06567094 -.21523927 -.018034656 .009165896 .02333628 .037206687 .05158065 .07111476 .09325614 .12179398 .18044484 .37819275 .0956796 .459604 "country1" 3 2012 .08633114 .05410804 -.2125947 -.02891541 .0017645848 .01650355 .02816639 .04203522 .05897056 .0816034 .11296052 .16214398 .3292475 .09428854 .224693 "country1" 3 2013 .0834767 .05123372 -.2387874 -.03119109 .0019640152 .01536021 .02625349 .04114122 .05806222 .07941144 .10745727 .1608692 .3421259 .09801974 -.4414992 "country1" 4 2002 .0761424 .04321241 -.177959 -.03989331 -.005459618 .011226195 .025578195 .035309874 .05130946 .06777202 .09763467 .13936985 .26399398 .08202033 .08701523 "country1" 4 2003 .08296005 .04989164 -.249568 -.03377722 -.001527387 .015984016 .028352024 .0409112 .05579127 .07867818 .11061735 .15606412 .32728675 .09541795 -.1603687 "country1" 4 2004 .08324701 .05306102 -.25195894 -.03727824 -.00247604 .016100459 .028765943 .04168353 .05927675 .0811041 .11040893 .1646192 .340127 .09729557 .48081565 "country1" 4 2005 .08302285 .0516314 -.1826295 -.0373856 -.0032770515 .013688901 .02764646 .03913922 .05523873 .07526898 .10469875 .1656168 .3512687 .09299619 .8096488 "country1" 4 2006 .07876872 .05608401 -.19670513 -.022336854 .007244009 .01963087 .031917892 .04411551 .05823285 .07945644 .1130261 .16178103 .3195939 .0882971 .10611613 "country1" 4 2007 .08401462 .062558375 -.14115284 -.01857368 .008588405 .022717465 .03380351 .04705557 .06309705 .08109027 .11451538 .17888045 .3670835 .09380407 .17359707 "country1" 4 2008 .0767868 .04051908 -.22466592 -.04930649 -.01111339 .006674293 .021993525 .035296552 .0464601 .06375654 .0920365 .14876674 .317237 .0949736 -.20016664 "country1" 4 2009 .07985446 .02432179 -.28827405 -.07491066 -.028332643 -.0014370215 .014198358 .02642919 .03908671 .05639958 .08587336 .12950477 .26133117 .10249417 -1.857381 "country1" 4 2010 .0771031 .033876687 -.25494134 -.0571739 -.013892468 .006264115 .01889995 .031646583 .04544014 .06087434 .08839293 .13732244 .27799308 .09087478 -.4032592 "country1" 4 2011 .07228889 .036778066 -.2190525 -.05432998 -.007518314 .009173376 .02291244 .031688064 .04528688 .06134728 .0875039 .13274461 .26848385 .08566634 .07688054 "country1" 4 2012 .07312051 .03146846 -.24487136 -.05917589 -.01378863 .0043033287 .01992145 .03029441 .04345836 .05948703 .08526755 .13196686 .24860907 .08567636 -.3801258 "country1" 4 2013 .070701174 .03560501 -.2621918 -.0415739 -.002698769 .010468404 .02260456 .033873614 .04626832 .062856644 .0882164 .12761183 .25532335 .08643822 -1.339375 "country1" 5 2002 .07495708 .02520862 -.54284286 -.09241012 -.015848434 .014829884 .02973453 .036501102 .0503041 .065220065 .10102759 .13520499 .2712313 .13938561 -1.8459368 "country1" 5 2003 .09014196 .01702821 -.5254196 -.11733481 -.021822996 -.0003664067 .01762901 .03256086 .04661847 .06621059 .0886427 .138838 .23224524 .12431087 -2.059987 "country1" 5 2004 .07836258 .030706225 -.486733 -.0643566 -.013809043 .008418812 .022450604 .032229446 .04908463 .06767744 .09548683 .15153825 .28345758 .11342914 -1.645751 "country1" 5 2005 .0861647 .0456177 -.24846733 -.04835508 -.005504063 .011466694 .029394565 .041956 .05216737 .073281184 .10297295 .15567893 .30322134 .09703737 -.19675295 "country1" 5 2006 .08527346 .04259104 -.3406084 -.05515092 -.003915444 .0130605 .0257545 .03838684 .05472883 .07750607 .10679445 .1797755 .3313127 .1092799 -.7410077 "country1" 5 2007 .106355 .04367311 -.3626013 -.05207738 -.011300126 .013037896 .02928171 .04319012 .05673432 .08139578 .1196597 .16461383 .2967354 .11696617 -1.2954075 "country1" 5 2008 .09212613 .02960361 -.3773454 -.07981354 -.02162791 .004869143 .02218063 .03566789 .04917278 .0677662 .0999489 .1535571 .3709346 .12594992 -1.215883 "country1" 5 2009 .09347544 .008010149 -.398222 -.10661717 -.04685502 -.017014416 .0026338855 .018173099 .03667682 .05357634 .08038546 .12665701 .26347235 .11808112 -1.311399 "country1" 5 2010 .10045807 .04169214 -.4799534 -.06531346 -.014094308 .00976391 .02457494 .03903105 .06030878 .08278175 .11837518 .17267238 .4161286 .12917438 -1.3699483 "country1" 5 2011 .09015185 .03793002 -.2941589 -.0796479 -.025694465 .006509672 .024154123 .034732953 .05051185 .066899925 .1060098 .15872994 .4218395 .12167666 -.177884 "country1" 5 2012 .10405073 .020764906 -.4920145 -.1103046 -.04689472 -.006201227 .0108103 .03058775 .04557512 .06009704 .0900197 .13889624 .4213161 .13758357 -.7562149 "country1" 5 2013 .10087954 .03914583 -.3267701 -.09223686 -.017802164 .00645366 .01980037 .03638824 .05357252 .08057185 .1113605 .1594688 .357477 .11130723 -.3299317 "country1" 6 2002 .15551113 -.0015128036 -.9861695 -.23422626 -.09157452 -.02574774 .005648563 .030147437 .04734012 .07421834 .12450182 .2032906 .49161536 .2309334 -1.8014426 "country1" 6 2003 .13311383 .04943813 -.7329614 -.0984272 -.035090268 .00725207 .027194576 .04690337 .070626006 .1033741 .1519632 .2361128 .5298856 .1881927 -1.1764524 "country1" 6 2004 .14025663 .06953695 -.6089267 -.07769976 -.006876392 .02024381 .04059287 .05730909 .08751666 .12705103 .18164724 .2725083 .55344474 .1961026 -1.383877 "country1" 6 2005 .14150476 .09015566 -.3744736 -.04474829 .00592837 .023135614 .04034172 .063757025 .09184575 .1201751 .1900424 .2795264 .5702373 .1602521 .20194773 "country1" 6 2006 .14562097 .09568833 -.3664871 -.03781585 .002532345 .02752266 .04752464 .07262954 .10324946 .14032722 .19811156 .2920247 .5648109 .17351435 -1.1401423 "country1" 6 2007 .1546874 .09468355 -.5731731 -.04282883 .00490917 .028524883 .05253023 .07552305 .10753161 .14285591 .1987092 .2941934 .6488358 .18190037 -.9041301 "country1" 6 2008 .1502317 .08617527 -.384954 -.06099223 .0005512537 .02050596 .04061357 .06654939 .09683648 .13387442 .18686873 .28546742 .5735001 .15950885 -.1621773 "country1" 6 2009 .13553189 .0643158 -.3345598 -.07823925 -.018385125 .010035722 .033229034 .0548277 .08312485 .1074566 .1629301 .24197076 .4803675 .1551005 -.5962112 "country1" 6 2010 .14100188 .08571576 -.4162999 -.04232148 .0021689765 .0250996 .0449493 .07434507 .10315592 .13182358 .18623044 .25697127 .4720738 .1570774 -.9716018 "country1" 6 2011 .13679317 .07770913 -.3597609 -.04709454 .003121098 .02587223 .0429403 .06884782 .09546895 .12662192 .17406613 .2428157 .4214878 .14266212 -.43358555 "country1" 6 2012 .12152443 .0731587 -.28072646 -.06065452 .0015573872 .02034806 .041102 .062916316 .0807948 .11104132 .16682246 .2331359 .49981135 .14730342 -.4163422 "country1" 6 2013 .13844165 .07871928 -.2737282 -.06624124 .001353807 .02341374 .04054291 .05893755 .08399507 .1149027 .17586604 .25976494 .52363825 .14493726 .27518913 "country1" 7 2002 .02344899 .026387393 -.04817886 -.00026271402 .007709973 .01159545 .014416783 .017997421 .020438934 .026012104 .0380311 .070699014 .14753298 .03779557 1.8629453 "country1" 7 2003 .01948738 .023362506 -.13614367 .0009207938 .007960506 .014618172 .016186593 .019683685 .02342207 .02903811 .034238007 .05958128 .1600087 .04262414 .25840795 "country1" 7 2004 .017065156 .0296802 -.0483893 .005766061 .010783174 .015157515 .017004084 .019645166 .022225374 .02753399 .035139382 .05704641 .1922711 .0449929 1.51958 "country1" 7 2005 .02343092 .035237115 -.0025658875 .008471952 .013370572 .016039634 .01951754 .02228422 .025355317 .033959452 .04176835 .07379334 .1860302 .04051349 2.639068 "country1" 7 2006 .018187212 .031978723 -.0040581995 .00374377 .01145338 .014309038 .017752815 .020396894 .023468876 .029092547 .037120704 .07688147 .2059884 .03987208 2.762503 "country1" 7 2007 .016519288 .02452854 -.003831864 .0045678653 .01013728 .01350723 .016271248 .01893144 .024106493 .027803376 .03138601 .04369557 .13928194 .02564592 2.586404 "country1" 7 2008 .016581766 .02089577 -.05096121 -.003336258 .005423544 .01120773 .01549376 .016986404 .01945188 .022048887 .02929073 .04303933 .19630224 .03282633 3.416464 "country1" 7 2009 .02087052 .019622535 -.09104105 -.002864744 .003614588 .01098208 .014170581 .016713979 .020361053 .024909457 .031353876 .05749472 .13501173 .03838194 .1897972 "country1" 7 2010 .02067431 .01718142 -.08432898 -.003679725 .003956329 .007741359 .011588477 .015214113 .017895484 .02275875 .03047551 .04248103 .16457695 .033970263 1.0466878 "country1" 7 2011 .018680075 .02132724 -.05451318 -.0015694636 .002956528 .0079174675 .010799267 .015250576 .017613191 .02114769 .02919084 .05091917 .15221746 .036750685 2.5372415 "country1" 7 2012 .02310909 .015398523 -.11775614 -.0019766015 .003142858 .006732693 .010447594 .013900735 .01730142 .021777134 .032294918 .05517171 .1191701 .03778702 -.9736355 "country1" 7 2013 .019181177 .02407885 -.10586757 .0006388281 .003718009 .007251433 .00879842 .012794668 .016371043 .019228047 .036122106 .06542239 .21966584 .04692483 2.026585 "country1" 8 2002 .09758225 .04860054 -.34806165 -.03968321 -.005002063 .0010799654 .011774253 .03057411 .04954733 .08121374 .11843142 .18785445 .4016522 .12495005 -.3339961 "country1" 8 2003 .10736115 .05905765 -.26950705 -.02626834 -.0003736748 .005211414 .02303741 .04173001 .06086683 .0918174 .13451464 .20450263 .39540935 .11651483 -.27917758 "country1" 8 2004 .12908033 .07890072 -.2120128 -.007832929 .0006471635 .00995666 .02671138 .04862392 .073536895 .10821618 .15163314 .2266289 .56276006 .13264199 .8849259 "country1" 8 2005 .11973336 .07477309 -.19758555 -.008265283 .0014072504 .012046594 .028032156 .0474262 .07443161 .102713 .149738 .21773097 .4119495 .12191124 .6018402 "country1" 8 2006 .12210908 .07778075 -.25208467 -.006210989 .0015268747 .014100658 .029396104 .04973927 .07522817 .10406048 .1554419 .24320573 .4577823 .1268722 .16079146 "country1" 8 2007 .13570377 .0935859 -.2759366 -.004323612 .003062029 .017212022 .03438036 .05734251 .08668733 .12080176 .18112764 .2659954 .54909974 .1509802 .8814493 "country1" 8 2008 .14388527 .08281237 -.3259705 -.01483257 .00018748287 .010374612 .029125927 .04990584 .07548323 .12377079 .18082704 .26422888 .5835321 .16099136 -.08383115 "country1" 8 2009 .11297017 .063954026 -.3390397 -.04758407 -.0007829008 .004334792 .01950402 .04041741 .06548718 .09611692 .13986124 .2269507 .4819754 .1415728 .7567139 "country1" 8 2010 .12202451 .07672725 -.3441372 -.01897465 .001601446 .01283176 .028038885 .04413277 .06803283 .10402051 .1565497 .2470032 .5929802 .14703546 .6752805 "country1" 8 2011 .1344569 .07926615 -.3060918 -.02501058 .0003448713 .011517095 .025222395 .04880414 .07692464 .10666019 .1651397 .24359463 .58984596 .15447646 .4033714 "country1" 8 2012 .1229187 .07583922 -.27604997 -.03541175 -.000033627497 .011534863 .03034898 .0495019 .073038 .10432 .1569358 .2338867 .5515265 .14502345 .822567 "country1" 8 2013 .12012394 .07395481 -.3024483 -.03034107 .0007153547 .013651394 .02566655 .04527388 .07144747 .10475671 .15856338 .23830578 .51256603 .14166538 -.09837282 "country1" 9 2002 .09249414 .019332645 -.6245538 -.12785609 -.024545455 .0034819865 .01940565 .033172566 .04820438 .07227254 .09969687 .149458 .34599435 .14672501 -2.07964 "country1" 9 2003 .10200325 .0517487 -.6790662 -.06198534 -.0046276283 .01488697 .031439144 .0416185 .06138353 .08557361 .12955518 .2135396 .4560108 .1549058 -1.0063652 "country1" 9 2004 .1533213 .08252954 -.4158163 -.04906107 -.0016328752 .024324076 .03955643 .05171191 .08163448 .1199678 .19399236 .2773228 .474212 .14921325 -.04565446 "country1" 9 2005 .14446907 .0915531 -.28905177 -.05279396 .004465094 .028686585 .04737 .06207036 .08607858 .1356438 .18808778 .298928 .55588114 .15156996 .4122129 "country1" 9 2006 .14855357 .11205864 -.19585153 -.018297425 .015694752 .03737482 .05515214 .0713785 .10074518 .1510019 .2085725 .3294408 .6088476 .15686506 .8955406 end
Comment