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From | "Ross, Andrew" <A.Ross2@napier.ac.uk> |
To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
Subject | st: Hausman Query |
Date | Wed, 5 Jan 2011 08:50:03 +0000 |
Hello I am currently using Stata to investigate new firm formation for 32 Scottish regions over a 10 year period. I was wondering, if you might offer your opinion on a Stata related matter, that I have encountered? As you can see from the attached output I've run a fixed and random effects model and followed this by the hausman test. However, the hausman highlights a 'note', as you will see from the attached output. I was wondering, if you could shed any light on this note and what is means? I have asked four other people and they do not know. One suggested it may be a result of over parameterisation given the small size of the panel, but they are not sure. Many thanks. Andrew xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ_b > s Pop_density Gov_sector Small_bus, fe vce (robust) Fixed-effects (within) regression Number of obs = 320 Group variable: Region Number of groups = 32 R-sq: within = 0.2061 Obs per group: min = 10 between = 0.0019 avg = 10.0 overall = 0.0030 max = 10 F(11,277) = 3.10 corr(u_i, Xb) = -0.9507 Prob > F = 0.0006 (Std. Err. adjusted for clustering on Region) ------------------------------------------------------------------------------ | Robust Lab_TP | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------- -------------+------ Wge_grow | -.0265289 .0270548 -0.98 0.328 -.079788 .0267303 Pop_grow | .4054536 .5845519 0.69 0.489 -.7452749 1.556182 Log_unempl~d | 4.109563 4.222209 0.97 0.331 -4.20213 12.42126 NVQ4_pop | -.0295052 .0431429 -0.68 0.495 -.1144348 .0554243 House_price | .0000483 .0000121 3.99 0.000 .0000245 .0000722 LQ_agric | .1687096 .4963323 0.34 0.734 -.8083529 1.145772 LQ_man | -.1523606 .4695697 -0.32 0.746 -1.076739 .7720178 LQ_bs | 2.506032 1.647939 1.52 0.129 -.7380422 5.750107 Pop_density | .0236083 .0110802 2.13 0.034 .0017962 .0454204 Gov_sector | -.0001643 .0309392 -0.01 0.996 -.0610701 .0607415 Small_bus | .3920981 .4383467 0.89 0.372 -.470816 1.255012 _cons | -32.9382 42.48215 -0.78 0.439 -116.5671 50.69067 -------------+---------------------------------------------------------- -------------+------ sigma_u | 17.794849 sigma_e | 2.771809 rho | .9763121 (fraction of variance due to u_i) ------------------------------------------------------------------------------ . estimates store fixed . xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ > _bs Pop_density Gov_sector Small_bus, re vce (robust) Random-effects GLS regression Number of obs = 320 Group variable: Region Number of groups = 32 R-sq: within = 0.1667 Obs per group: min = 10 between = 0.6091 avg = 10.0 overall = 0.4986 max = 10 Random effects u_i ~ Gaussian Wald chi2(12) = 3152.08 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on Region) ------------------------------------------------------------------------------ | Robust Lab_TP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------- -------------+------ Wge_grow | -.0254291 .0298964 -0.85 0.395 -.084025 .0331667 Pop_grow | .8175778 .5211693 1.57 0.117 -.2038953 1.839051 Log_unempl~d | -4.643811 2.993296 -1.55 0.121 -10.51056 1.222941 NVQ4_pop | .008423 .0484623 0.17 0.862 -.0865613 .1034074 House_price | .0000265 .0000108 2.46 0.014 5.39e-06 .0000476 LQ_agric | .7014816 .4126435 1.70 0.089 -.1072848 1.510248 LQ_man | .2703715 .5041589 0.54 0.592 -.7177617 1.258505 LQ_bs | 4.506697 1.720704 2.62 0.009 1.13418 7.879214 Pop_density | .0023373 .0006452 3.62 0.000 .0010727 .0036018 Gov_sector | -.0345817 .034529 -1.00 0.317 -.1022574 .0330939 Small_bus | .6680098 .1846674 3.62 0.000 .3060683 1.029951 _cons | -42.7439 17.37493 -2.46 0.014 -76.79813 -8.689662 -------------+---------------------------------------------------------- -------------+------ sigma_u | 2.2647466 sigma_e | 2.771809 rho | .40033378 (fraction of variance due to u_i) ------------------------------------------------------------------------------ . estimates store random . hausman fixed random Note: the rank of the differenced variance matrix (10) does not equal the number of coefficients being tested (11); be sure this is what you expect, or there may be problems computing the test. Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale. ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fixed random Difference S.E. -------------+---------------------------------------------------------- -------------+------ Wge_grow | -.0265289 -.0254291 -.0010997 . Pop_grow | .4054536 .8175778 -.4121243 .2647328 Log_unempl~d | 4.109563 -4.643811 8.753374 2.977789 NVQ4_pop | -.0295052 .008423 -.0379283 . House_price | .0000483 .0000265 .0000218 5.53e-06 LQ_agric | .1687096 .7014816 -.5327721 .2758099 LQ_man | -.1523606 .2703715 -.4227322 . LQ_bs | 2.506032 4.506697 -2.000664 . Pop_density | .0236083 .0023373 .021271 .0110614 Gov_sector | -.0001643 -.0345817 .0344174 . Small_bus | .3920981 .6680098 -.2759117 .3975498 ------------------------------------------------------------------------------ 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(10) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 5.58 Prob>chi2 = 0.8493 (V_b-V_B is not positive definite) Andrew Ross PhD Candidate School of Accounting, Economics & Statistics Napier University Business School Craiglockhart Campus Room 1/38 EH14 IDJ Email: a.ross2@napier.ac.uk Edinburgh Napier University is Edinburgh's top university for graduate employability (HESA 2010), and proud winner of the Queen's Anniversary Prize for Higher and Further Education 2009, awarded for innovative housing construction for environmental benefit and quality of life. 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