This is the output of my Hausman test.. what does it mean by model fitted on these data does not meet asymptotic assumptions.
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This is the output of my Hausman test.. what does it mean by model fitted on these data does not meet asymptotic assumptions. -
It means what the error message says. The statistic is supposed to be asymptotically Chi-squared distributed (a non-negative random variable), but the calculated statistic is negative. -
There is an issue here then. How do I take care of this problem?
Using xtoverid is the solution?Comment
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Anuradha:
yes, the community-contributed command -xtoverid- is a good alternative (checking the -re- specification only is enough; if -xtoverid- outcome reaches statistical significance, you should switch to -fe- specification).
Please remember that it does not support -fvvralist- notation.Kind regards,
Carlo
(Stata 19.0)Comment
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Okay Sir Carlo Lazzaro . How do I report it in the methodology part of my paper. The Hausman Test did not work and its a standard test. I can't write I used xtoverid as its only a stata command.Comment
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Anuradha:
the -xtoverid- helpfile gives you the full reference of this community-contributed command, that you can well include in your research report/paper:
Schaffer, M.E., Stillman, S. 2010. xtoverid: Stata module to calculate tests of overidentifying restrictions after xtreg, xtivreg, xtivreg2 and xthtaylor
http://ideas.repec.org/c/boc/bocode/s456779.html
Kind regards,
Carlo
(Stata 19.0)Comment
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Apart from citing the user written command -xtoverid- as Carlo explained above (user written commands should be cited, they are research as any other), you can also see in the help file, and to use the key reference on which -xtoverid- is based.
Arellano, M. 1993. On the testing of correlated effects with panel data. Journal of Econometrics, Vol. 59, Nos. 1-2, pp. 87-97.Comment
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The xtoverid is a bit of a black box. I like using the Mundlak approach, where one includes the time averages of all time-varying variables, estimates the equation by random effects, and tests the time averages. This reproduces the fixed effects estimates on all time-varying variables. Plus, one can see which time averages are important. I cover the general unbalanced case in my 2019 Journal of Econometrics paper on correlated random effects models.Comment
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Indeed Professor Wooldridge, this would be the easier approach here. And I was about to propose this to Anuradha Saikia, but then after I tried it, I remembered that one does not achieve exact equivalence for non-balanced panels.
What I tried is another version of the Mundlak's approach which I explain in the paper attached (which I submitted to Stata Journal in year 2008, I think I got a referee who did not understand the issue and I was too young to care fighting the powers that be, I had more fun stuff to do back in those days). The other version of the Mundlak's approach is just estimating the equation that you describe by OLS, then the slopes on the time averages show you the difference between the Fixed Effects and the Between estimator, and the slopes on the time varying covariates have to be equal to the Fixed Effects estimates (but only in balanced panels, so I got quite some difference). So a test of joint significance of the slopes on the time averages is a Hausman test of FE vs BE model.
Anyways, even if we go with your version of the Mundlak's approach, we still get some slight differences for unbalanced panels:
So what we see above is that the estimates for unbalanced panels are a bit different, and this is hard to explain to a novice. (That asymptotic results do not exactly hold in finite samples.)Code:. webuse nlswork, clear (National Longitudinal Survey. Young Women 14-26 years of age in 1968) . xtset idcode panel variable: idcode (unbalanced) . xtreg ln_w age ttl_exp tenure 2.race grade, fe note: 2.race omitted because of collinearity note: grade omitted because of collinearity Fixed-effects (within) regression Number of obs = 28,099 Group variable: idcode Number of groups = 4,697 R-sq: Obs per group: within = 0.1443 min = 1 between = 0.2745 avg = 6.0 overall = 0.1924 max = 15 F(3,23399) = 1315.26 corr(u_i, Xb) = 0.1651 Prob > F = 0.0000 ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | -.0030427 .0008644 -3.52 0.000 -.0047369 -.0013484 ttl_exp | .029036 .0014505 20.02 0.000 .026193 .031879 tenure | .0116574 .0009249 12.60 0.000 .0098444 .0134704 | race | black | 0 (omitted) grade | 0 (omitted) _cons | 1.547951 .0181798 85.15 0.000 1.512317 1.583584 -------------+---------------------------------------------------------------- sigma_u | .3751722 sigma_e | .29556813 rho | .61703248 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(4696, 23399) = 7.64 Prob > F = 0.0000 . qui for var age ttl_exp tenure: egen meanX = mean(X), by(idcode) . xtreg ln_w age ttl_exp tenure mean* 2.race grade, re Random-effects GLS regression Number of obs = 28,099 Group variable: idcode Number of groups = 4,697 R-sq: Obs per group: within = 0.1443 min = 1 between = 0.4329 avg = 6.0 overall = 0.3250 max = 15 Wald chi2(8) = 7538.32 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | -.0030268 .0008614 -3.51 0.000 -.0047152 -.0013385 ttl_exp | .0290337 .0014457 20.08 0.000 .0262003 .0318672 tenure | .0116424 .0009222 12.62 0.000 .0098349 .01345 meanage | -.0026319 .00142 -1.85 0.064 -.0054151 .0001513 meanttl_exp | -.0008391 .0025701 -0.33 0.744 -.0058764 .0041982 meantenure | .0165731 .0024676 6.72 0.000 .0117366 .0214095 | race | black | -.062727 .0103071 -6.09 0.000 -.0829286 -.0425254 grade | .0701835 .0020152 34.83 0.000 .0662339 .0741332 _cons | .709563 .0346377 20.49 0.000 .6416744 .7774516 -------------+---------------------------------------------------------------- sigma_u | .27539065 sigma_e | .29556813 rho | .46470444 (fraction of variance due to u_i) ------------------------------------------------------------------------------
For my interpretation of the Mundlak's approach the differences were even harder to explain:
Code:. reg ln_w age ttl_exp tenure mean* 2.race grade, noheader ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | -.002911 .0011444 -2.54 0.011 -.0051542 -.0006679 ttl_exp | .028964 .001921 15.08 0.000 .0251989 .0327292 tenure | .0115805 .0012274 9.44 0.000 .0091748 .0139861 meanage | -.0022723 .0013232 -1.72 0.086 -.0048658 .0003212 meanttl_exp | -.0023782 .0022615 -1.05 0.293 -.0068108 .0020545 meantenure | .0171518 .0017178 9.98 0.000 .0137848 .0205188 | race | black | -.0806084 .0052841 -15.25 0.000 -.0909655 -.0702513 grade | .0708902 .0011003 64.43 0.000 .0687336 .0730468 _cons | .7061531 .0197196 35.81 0.000 .6675017 .7448045 ------------------------------------------------------------------------------
Originally posted by Jeff Wooldridge View PostComment
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Joro Kolev : with the following I get exactly the same coefficients with FE and with Correlated Random Effects.
I think that you have forgotten to select only the "complete" observations: those for which no value is missing for any of the variables concerned
This is done by the selection indicator.
On Edit:Code:webuse nlswork xtset idcode xtreg ln_w age ttl_exp tenure 2.race grade, fe gen s = (ln_wage != .) & (age != .) & (ttl_exp != .) & (tenure != .) & (race != .) & (grade != .) egen agebar = mean(age) if s, by(idcode) egen ttl_expbar = mean(ttl_exp) if s, by(idcode) egen tenurebar = mean(tenure) if s, by(idcode) egen racebar = mean(race) if s, by(idcode) egen gradebar = mean(grade) if s, by(idcode) xtreg ln_wage age ttl_exp tenure 2.race grade agebar ttl_expbar tenurebar racebar gradebar, re
should beCode:egen racebar = mean(race) if s, by(idcode)
ICode:egen racebar = mean(2.race) if s, by(idcode)
Last edited by Eric de Souza; 21 Sep 2020, 08:46.Comment
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Thank you, Eric. I was about to write the same thing. I emphasize this point in my paper. I admit that it tripped me up for several years. Also important is that, if the model includes time dummies or any aggregate time variables, their time averages must also be included.
In fact, using different observations to compute the time averages is not even consistent, in general, when the complete cases FE estimator is.Comment
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Addition to #11 (posted by me):
Ssince 2.race and grade are time constant, racebar and gradebar can be dropped and, in fact, are dropped. It was because racebar was not dropped that I realised my mistake and edited my previous post (#11)
I have also added time dummies to illustrate the point made by Jeff Wooldridge (#12)
Code:log using CRE_unbalanced_panel.log, replace webuse nlswork keep if (year == 68) | (year == 69) | (year ==70) | (year == 71) tab year, gen(year) xtset idcode xtreg ln_w age ttl_exp tenure 2.race grade year2-year4, fe gen s = (ln_wage != .) & (age != .) & (ttl_exp != .) & (tenure != .) & (race != .) & (grade != .) egen agebar = mean(age) if s, by(idcode) egen ttl_expbar = mean(ttl_exp) if s, by(idcode) egen tenurebar = mean(tenure) if s, by(idcode) egen year1bar = mean(year1) if s, by (idcode) egen year2bar = mean(year2) if s, by (idcode) egen year3bar = mean(year3) if s, by (idcode) egen year4bar = mean(year4) if s, by (idcode) xtreg ln_wage age ttl_exp tenure 2.race grade year2-year4 agebar ttl_expbar tenurebar year2bar year3bar year4bar, re clear log close
Last edited by Eric de Souza; 21 Sep 2020, 10:39.Comment
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Thank you Professor Jeff Wooldridge Eric de Souza for enlightening me to new ways of looking into the problem. I am quite novice and still learning. Prof Wooldridge if you could share the paper you mentioned .
In my case I have a strongly balanced panel though. Everything goes smooth until the Hausman Test and I guess the iteration is not done properly in the command.
Comment
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@Jeff Wooldridge @Eric de Souza @Joro Kolev I add "if e(sample)"options on the code of @Eric de Souza to ensure the same observations used in xtreg, fe robust and xtreg, re robust. And also get get exactly the same coefficients with FE and with Correlated Random Effects.Maybe adding "if e(sample)" a simpler way to guarantee the complete observations just as @Jeff Wooldridge said.This kind of method also tells us the observations we use to FE and CRE should be exactly the same.
Code:webuse nlswork xtset idcode xtreg ln_w age ttl_exp tenure 2.race grade, fe r Fixed-effects (within) regression Number of obs = 28,099 Group variable: idcode Number of groups = 4,697 R-sq: Obs per group: within = 0.1443 min = 1 between = 0.2745 avg = 6.0 overall = 0.1924 max = 15 F(3,4696) = 544.06 corr(u_i, Xb) = 0.1651 Prob > F = 0.0000 (Std. Err. adjusted for 4,697 clusters in idcode) ------------------------------------------------------------------------------ | Robust ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | -0.003 0.001 -2.35 0.019 -0.006 -0.001 ttl_exp | 0.029 0.002 12.72 0.000 0.025 0.034 tenure | 0.012 0.001 7.93 0.000 0.009 0.015 | race | black | 0.000 (omitted) grade | 0.000 (omitted) _cons | 1.548 0.027 56.78 0.000 1.494 1.601 -------------+---------------------------------------------------------------- sigma_u | .3751722 sigma_e | .29556813 rho | .61703248 (fraction of variance due to u_i) ------------------------------------------------------------------------------ egen agebar = mean(age) , by(idcode) egen ttl_expbar = mean(ttl_exp) , by(idcode) egen tenurebar = mean(tenure) , by(idcode) egen racebar = mean(race) , by(idcode) egen gradebar = mean(grade) , by(idcode) xtreg ln_wage age ttl_exp tenure 2.race grade agebar ttl_expbar tenurebar racebar gradebar if e(sample), re r Random-effects GLS regression Number of obs = 28,099 Group variable: idcode Number of groups = 4,697 R-sq: Obs per group: within = 0.1443 min = 1 between = 0.4339 avg = 6.0 overall = 0.3252 max = 15 Wald chi2(9) = 4529.55 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for 4,697 clusters in idcode) ------------------------------------------------------------------------------ | Robust ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | -0.003 0.001 -2.34 0.019 -0.006 -0.000 ttl_exp | 0.029 0.002 12.72 0.000 0.025 0.034 tenure | 0.012 0.001 7.92 0.000 0.009 0.015 | race | black | -0.114 0.025 -4.50 0.000 -0.163 -0.064 grade | 0.070 0.002 31.31 0.000 0.066 0.075 agebar | -0.003 0.002 -1.57 0.116 -0.006 0.001 ttl_expbar | -0.001 0.003 -0.28 0.777 -0.007 0.005 tenurebar | 0.017 0.003 6.12 0.000 0.011 0.022 racebar | 0.053 0.024 2.22 0.027 0.006 0.099 gradebar | 0.000 (omitted) _cons | 0.655 0.044 14.86 0.000 0.569 0.742 -------------+---------------------------------------------------------------- sigma_u | .27510497 sigma_e | .29556813 rho | .4641881 (fraction of variance due to u_i) ------------------------------------------------------------------------------Best regards.
Raymond Zhang
Stata 17.0,MPComment
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