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From |
Clive Nicholas <clivelists@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: fixed vs random effect model |

Date |
Mon, 5 Jul 2010 01:32:14 +0100 |

Martin Weiss replied: > What`s your rule of thumb then, Steve, for the RE model to be considered? In > this case, you have -.15, do you still use RE? If you -bootstrap- the thing, > the CI covers 0 comfortably... > > > *********** > webuse grunfeld, clear > xtset company year > bs e(corr), reps(200) seed(32456): xtreg invest mvalue kstock, i(company) fe > *********** For me -- speaking as an idiot non-econometrican -- the key, as I implied earlier, would be to use both -hausman- and that indicator in -xtreg, fe- together: . webuse grunfeld, clear . xtreg invest mvalue kstock, i(company) fe Fixed-effects (within) regression Number of obs = 200 Group variable (i): company Number of groups = 10 R-sq: within = 0.7668 Obs per group: min = 20 between = 0.8194 avg = 20.0 overall = 0.8060 max = 20 F(2,188) = 309.01 corr(u_i, Xb) = -0.1517 Prob > F = 0.0000 ^^^^^^^^^ ------------------------------------------------------------------------------ invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mvalue | .1101238 .0118567 9.29 0.000 .0867345 .1335131 kstock | .3100653 .0173545 17.87 0.000 .2758308 .3442999 _cons | -58.74393 12.45369 -4.72 0.000 -83.31086 -34.177 -------------+---------------------------------------------------------------- sigma_u | 85.732501 sigma_e | 52.767964 rho | .72525012 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(9, 188) = 49.18 Prob > F = 0.0000 . est store fixed . qui xtreg invest mvalue kstock, re . est store random . hausman fixed . ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fixed random Difference S.E. -------------+---------------------------------------------------------------- mvalue | .1101238 .1097811 .0003427 .0055213 kstock | .3100653 .308113 .0019524 .0024516 ------------------------------------------------------------------------------ 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(2) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 2.33 Prob>chi2 = 0.3119 ^^^^^^^^^ Here, the two statistics reinforce the same conclusion: an RE model could be fit to this data. But lucky is the researcher who has such data to play with; certainly not me. An alternative example (although one could say this is a selective model, but imagine it was the only data we had): . webuse nlswork . xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work, i(idcode) fe Fixed-effects (within) regression Number of obs = 13550 Group variable (i): idcode Number of groups = 4001 R-sq: within = 0.1325 Obs per group: min = 1 between = 0.2106 avg = 3.4 overall = 0.1744 max = 11 F(8,9541) = 182.14 corr(u_i, Xb) = 0.1774 Prob > F = 0.0000 ^^^^^^^^ ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0046006 .0006602 6.97 0.000 .0033066 .0058947 nev_mar | -.0295329 .0118592 -2.49 0.013 -.0527794 -.0062863 south | -.0514096 .0169021 -3.04 0.002 -.0845412 -.018278 union | .1249207 .0089688 13.93 0.000 .1073399 .1425015 tenure | .0206019 .001053 19.56 0.000 .0185378 .0226661 hours | -.0015052 .0003538 -4.25 0.000 -.0021987 -.0008117 wks_ue | -.0001856 .0004326 -0.43 0.668 -.0010336 .0006624 wks_work | .0011162 .0001514 7.37 0.000 .0008193 .001413 _cons | 1.500244 .0237174 63.26 0.000 1.453753 1.546735 -------------+---------------------------------------------------------------- sigma_u | .39638065 sigma_e | .26223304 rho | .69556838 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(4000, 9541) = 5.85 Prob > F = 0.0000 . est store fixed . qui xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work, re . hausman fixed . ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fixed . Difference S.E. -------------+---------------------------------------------------------------- age | .0046006 .0029873 .0016134 .0002999 nev_mar | -.0295329 -.01738 -.0121529 .0066411 south | -.0514096 -.1348857 .0834761 .0135749 union | .1249207 .1377239 -.0128032 .0039118 tenure | .0206019 .0254651 -.0048631 .0004508 hours | -.0015052 -.0001432 -.001362 .0001495 wks_ue | -.0001856 -.0008195 .0006339 .0001434 wks_work | .0011162 .0016362 -.00052 .0000481 ------------------------------------------------------------------------------ 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(8) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 440.74 Prob>chi2 = 0.0000 ^^^^^^^^^ There's not much more difference in -corr(u_i, Xb)- than that observed in the Grunfeld data, and yet the Hausman test suggests a statistically significant difference between the two models fit to this data, this time favouring FE. No doubt the specialist econometricians will have more to say about this if they feel more needs to be said, which they probably will. -- Clive Nicholas [Please DO NOT mail me personally here, but at <clivenicholas@hotmail.com>. Please respond to contributions I make in a list thread here. Thanks!] "My colleagues in the social sciences talk a great deal about methodology. I prefer to call it style." -- Freeman J. Dyson. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: fixed vs random effect model***From:*amatoallah ouchen <at.ouchen@gmail.com>

**Re: st: fixed vs random effect model***From:*David Jacobs <jacobs.184@sociology.osu.edu>

**Re: st: fixed vs random effect model***From:*amatoallah ouchen <at.ouchen@gmail.com>

**Re: st: fixed vs random effect model***From:*Clive Nicholas <clivelists@googlemail.com>

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