Dane panelowe Model
Mar 19, 2016
Dane paneloweModel
Model grawitacyjny
Deklaracja danych panelowychWymiar czasu okrela si komend tis a wymiar obiektu komend iis
tis year iis pairid
Braki obserwacji w paneluxtdes
pairid: 1, 2, ..., 10193 n = 10194 year: 70, 75, ..., 95 T = 6 Delta(year) = 5; (95-70)/5 + 1 = 6 (pairid*year does not uniquely identify observations)
Distribution of T_i: min 5% 25% 50% 75% 95% max 1 1 2 4 6 6 616
Freq. Percent Cum. | Pattern ---------------------------+--------- 3823 37.50 37.50 | 111111Dla 37,50% jednostek, ktre 596 5.85 43.35 | ..1111pojawiy si w panelu 572 5.61 48.96 | .....1dysponujemy kompletem 6 obs. 434 4.26 53.22 | .11111 412 4.04 57.26 | 11111. 291 2.85 60.11 | ....1. 258 2.53 62.64 | ..1... 247 2.42 65.07 | ....11 244 2.39 67.46 | 11.... 3317 32.54 100.00 | (other patterns) ---------------------------+--------- 10194 100.00 | XXXXXX
Macierz przejciaxttrans nazwa_zmiennej
Estymator efektw losowychModel efektw losowych stosujemy, gdy:
efekty indywidualne nie s a skorelowane z regresorami xit
za., e efekt indywidualny jest realizacj pewnej zmiennej losowej o okrelonym rozkadzie.
xtreg ltrade lrgdp lpop ldist cu comcol comctry comlang colonial regional ll island
Random-effects GLS regression Number of obs = 31226Group variable (i): pairid Number of groups = 7961R-sq: within = 0.0308 Obs per group: min = 1 between = 0.6298 avg = 3.9 overall = 0.5761 max = 6Random effects u_i ~ Gaussian Wald chi2(11) = 12000.23corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000------------------------------------------------------------------------------ ltrade | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lrgdp | .8973097 .0128265 69.96 0.000 .8721703 .9224491 lpop | -.2821761 .0157241 -17.95 0.000 -.3129948 -.2513574 ldist | -1.189486 .029738 -40.00 0.000 -1.247771 -1.1312 cu | .4350876 .2064135 2.11 0.035 .0305245 .8396508 comcol | -.1916404 .0858374 -2.23 0.026 -.3598786 -.0234022 comctry | .8194063 .2761104 2.97 0.003 .2782399 1.360573 comlang | .4530111 .0722408 6.27 0.000 .3114217 .5946004 colonial | 2.587744 .2190961 11.81 0.000 2.158324 3.017165 regional | .1496601 .0897927 1.67 0.096 -.0263305 .3256506 ll | -.6674142 .0552592 -12.08 0.000 -.7757203 -.5591082 island | .0216517 .0431965 0.50 0.616 -.063012 .1063153 _cons | -6.97683 .3468105 -20.12 0.000 -7.656566 -6.297094-------------+---------------------------------------------------------------- sigma_u | 1.7722969 sigma_e | 1.2885209 rho | .65420233 (fraction of variance due to u_i)------------------------------------------------------------------------------
Zapisywanie wynikwest store random
xtsumR2 between jest duo wyszy od R2 within, co jest spowodowano tym, e dla wikszoci zmiennych zrnicowanie midzy jednostkami jest znacznie wysze ni dla poszczeglnych jednostek.xtsum ltrade
Variable | Mean Std. Dev. Min Max | Observations-----------------+-----------------------------------------------+----------------ltrade overall | 9.060543 3.348193 .1322796 19.39635 | N = 41061 between | 3.290938 .1322796 19.26711 | n = 10193 within | 1.213239 .0896298 16.43797 | T-bar = 4.02835
UWAGA! Dla tych zmiennych mona by byo obliczy rednie po pairid i odchylenia po tych zmiennych.
Graficzna prezentacja zalenoci midzy zmiennymi graph matrix ltrade cu ldist lrgdp
Test Breuscha-Pagana na wystpowanie efektw indywidualnych.
xttest0
Breusch and Pagan Lagrangian multiplier test for random effects:
ltrade[pairid,t] = Xb + u[pairid] + e[pairid,t]
Estimated results: | Var sd = sqrt(Var) ---------+----------------------------- ltrade | 10.87267 3.297373 e | 1.660286 1.288521 u | 3.141036 1.772297
Test: Var(u) = 0 chi2(1) = 11779.01 Prob > chi2 = 0.0000Testowanie hipotezy o istnieniu efektw indywidualnych sprowadza si do testowania hipotezy parametrycznej, e H0 : 2u= 0. Jeli hipoteza zerowa jest prawdziwa, to ui = 0 i liniowy model efektw nieobserwowalnych sprowadza si do modelu speniajcego zaoenia KMRL. W takim przypadku lepiej jest zamiast estymatora efektw losowych uy zwykego estymatora MNK. Jeli hipoteza zerowa zostanie odrzucona, wnioskujemy, e efekty indywidualne s istotne w modelu i w konsekwencji efektywniejszym estymatorem jest estymator efektw losowych.
Estymator efektw staych
Zakadamy: efekty indywidualne mog by skorelowane ze zmiennymi objaniajcymi.
Formujc model z czynnikami staymi zakada si, e rnice midzy jednostkami mog by uchwycone poprzez rnice w wyrazie wolnym. Uwzgldniony zostanie w ten sposb wpyw wszystkich zmiennych w czasie czynnikw, specyficznych dla kadej jednostki.
xtreg ltrade lrgdp lpop ldist cu comcol comctry comlang colonial regional ll island, fe
Fixed-effects (within) regression Number of obs = 31226Group variable (i): pairid Number of groups = 7961R-sq: within = 0.0500 Obs per group: min = 1 between = 0.0376 avg = 3.9 overall = 0.0387 max = 6
F(7,23258) = 175.01corr(u_i, Xb) = -1.0000 Prob > F = 0.0000------------------------------------------------------------------------------ ltrade | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- lrgdp | .773943 .0229327 33.75 0.000 .7289934 .8188926 lpop | -1.156388 .0484071 -23.89 0.000 -1.25127 -1.061507 ldist | 57609.99 86240.24 0.67 0.504 -111426.6 226646.6 cu | -.8935846 .5480874 -1.63 0.103 -1.967872 .1807029 comcol | (dropped) comctry | .6481806 .3340995 1.94 0.052 -.0066765 1.303038 comlang | -.1906378 .4885926 -0.39 0.696 -1.148312 .767036 colonial | (dropped) regional | -.0303829 .09633 -0.32 0.752 -.2191961 .1584303 ll | (dropped) island | (dropped) _cons | -472221.8 706906.1 -0.67 0.504 -1857804 913360.8-------------+---------------------------------------------------------------- sigma_u | 46551.107 sigma_e | 1.2885209 rho | 1 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(7960, 23258) = 7.54 Prob > F = 0.0000
Test Hausmana
Test Hausmanahausman . random
---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | . random Difference S.E.-------------+---------------------------------------------------------------- lrgdp | .773943 .8973097 -.1233667 .0190103 lpop | -1.156388 -.2821761 -.8742123 .0457821 ldist | 57609.99 -1.189486 57611.18 86240.24 cu | -.8935846 .4350876 -1.328672 .5077335 comctry | .6481806 .8194063 -.1712257 .1881105 comlang | -.1906378 .4530111 -.6436489 .4832225 regional | -.0303829 .1496601 -.1800429 .0348817------------------------------------------------------------------------------ b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 0.45 Prob>chi2 = 0.5041
Stay i specyficzny efekt zwizany z momentem obserwacjixi:xtreg ltrade cu ldist lrgdp lpop comlang regional comcol comctry colonial ll island i.yearRandom-effects GLS regression Number of obs = 31226Group variable (i): pairid Number of groups = 7961R-sq: within = 0.0976 Obs per group: min = 1 between = 0.6625 avg = 3.9 overall = 0.6306 max = 6
Random effects u_i ~ Gaussian Wald chi2(16) = 18430.59corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000------------------------------------------------------------------------------ ltrade | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- cu | 1.112545 .1928022 5.77 0.000 .7346598 1.490431 ldist | -1.244146 .0277457 -44.84 0.000 -1.298526 -1.189765 lrgdp | 1.326247 .0139995 94.74 0.000 1.298808 1.353685 lpop | -.5045464 .0152204 -33.15 0.000 -.5343778 -.474715 comlang | .4946473 .0673684 7.34 0.000 .3626077 .6266869 regional | .4599003 .0839523 5.48 0.000 .2953569 .6244437 comcol | .3828931 .0806516 4.75 0.000 .2248189 .5409672 comctry | .8659752 .2577852 3.36 0.001 .3607254 1.371225 colonial | 2.1163 .2044209 10.35 0.000 1.715643 2.516958 ll | -.332329 .0517973 -6.42 0.000 -.4338499 -.2308081 island | .3248042 .0405341 8.01 0.000 .2453589 .4042495 _Iyear_75 | -.1748795 .0263709 -6.63 0.000 -.2265656 -.1231935 _Iyear_80 | -.5083348 .027008 -18.82 0.000 -.5612696 -.4554 _Iyear_85 | -1.26094 .0275015 -45.85 0.000 -1.314842 -1.207038 _Iyear_90 | -1.435306 .0301363 -47.63 0.000 -1.494372 -1.376239 _Iyear_95 | -1.619971 .0328153 -49.37 0.000 -1.684288 -1.555654 _cons | -16.5935 .3599419 -46.10 0.000 -17.29897 -15.88803-------------+---------------------------------------------------------------- sigma_u | 1.7204213 sigma_e | 1.2527262 rho | .65350779 (fraction of variance due to u_i)------------------------------------------------------------------------------
Test Resetxtreg ltrade lrgdp lpop ldist cu comcol comctry comlang colonial regional ll island fit2 fit3Random-effects GLS regression Number of obs = 31226Group variable (i): pairid Number of groups = 7961R-sq: within = 0.0317 Obs per group: min = 1 between = 0.6496 avg = 3.9 overall = 0.5859 max = 6
Random effects u_i ~ Gaussian Wald chi2(13) = 12864.82corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000------------------------------------------------------------------------------ ltrade | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lrgdp | -1.244214 .1579944 -7.88 0.000 -1.553877 -.9345503 lpop | .4002097 .052442 7.63 0.000 .2974252 .5029942 ldist | 1.661203 .2100177 7.91 0.000 1.249576 2.07283 cu | -.518542 .2159019 -2.40 0.016 -.9417019 -.0953821 comcol | .25018 .089645 2.79 0.005 .0744789 .425881 comctry | -1.167509 .3103585 -3.76 0.000 -1.7758 -.5592171 comlang | -.6391032 .106948 -5.98 0.000 -.8487174 -.429489 colonial | -3.703678 .4993154 -7.42 0.000 -4.682318 -2.725038 regional | -.1262502 .0926495 -1.36 0.173 -.3078399 .0553395 ll | .9430459 .1295693 7.28 0.000 .6890947 1.196997 island | -.0523915 .0425347 -1.23 0.218 -.135758 .030975 fit2 | 70.97246 5.468811 12.98 0.000 60.25379 81.69113 fit3 | -39.28324 3.270625 -12.01 0.000 -45.69355 -32.87294 _cons | 16.43129 1.755942 9.36 0.000 12.9897 19.87287-------------+---------------------------------------------------------------- sigma_u | 1.7079146 sigma_e | 1.2866771 rho | .63793676 (fraction of variance due to u_i)------------------------------------------------------------------------------
Badanie resztSkewness -0.3893672Kurtosis 4.927893
Reszty musz by symetryczne wzgldem wartoci dopasowanych
Zbilansowanie paneluxtreg ltrade lrgdp lpop ldist cu comcol comctry comlang colonial regional ll island Random-effects GLS regression Number of obs = 14424Group variable (i): pairid Number of groups = 2404R-sq: within = 0.0513 Obs per group: min = 6 between = 0.7276 avg = 6.0 overall = 0.6180 max = 6Random effects u_i ~ Gaussian Wald chi2(11) = 5862.81corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000------------------------------------------------------------------------------ ltrade | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lrgdp | .8404294 .0167743 50.10 0.000 .8075524 .8733064 lpop | -.3204637 .0215761 -14.85 0.000 -.3627519 -.2781754 ldist | -1.063617 .0364111 -29.21 0.000 -1.134982 -.9922529 cu | .7274824 .6068931 1.20 0.231 -.4620062 1.916971 comcol | -.2370708 .1360379 -1.74 0.081 -.5037002 .0295586 comctry | .1838613 .6467118 0.28 0.776 -1.083671 1.451393 comlang | .2525556 .0800819 3.15 0.002 .095598 .4095132 colonial | 2.041308 .2103445 9.70 0.000 1.62904 2.453575 regional | .1451494 .0833236 1.74 0.082 -.0181618 .3084607 ll | -.3362375 .0781497 -4.30 0.000 -.489408 -.183067 island | .015717 .0529004 0.30 0.766 -.0879659 .1193998 _cons | -4.275765 .459591 -9.30 0.000 -5.176546 -3.374983-------------+---------------------------------------------------------------- sigma_u | 1.1760032 sigma_e | 1.0466633 rho | .55799494 (fraction of variance due to u_i)------------------------------------------------------------------------------
Grupowa heteroskedastycznoDla danych panelowych przyjmuje si GROUPWISE HETEROSCEDATICITY czyli za. wariancja skadnika losowego jest staa dla danej jednostki, natomiast moe si rni si pomidzy jednostkami.
TEST LM nie jest odporny na brak normalnoci resztsum LM p_value
Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- LM | 14424 12412.06 0 12412.06 12412.06 p_value | 14424 0 0 0 0
TEST skorygowany WALDA jest odporny na brak normalnoci resztsum W p_value1
Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- W | 14424 33.10704 166.5529 3.26e-07 3038.012 p_value1 | 14424 .9981855 .038677 8.81e-19 1
Test na czn istotno efektw losowych i istnienie autokorelacji 1 rzdu dla modelu REXttest1Joint Test:LM(Var(u)=0,rho=0) = 8562.63 Pr>chi2(2) = 0.0000
W modelu wystpuj efekty losowe i autokorelacja 1 rzdu.