fixed effect model — inconsistence between Stata's results and Wooldridge's textbook

[Chen Samulsion]

Dear Stata Users,

I have learned econometrics using Introductory Econometrics: A Modern Approach(5th Edition) written by Jeff Wooldridge. I found in webpage provided by Kit Baum an inconsistence between Stata's results and the textbook.

The webpage is below:
http://fmwww.bc.edu/gstat/examples/w...ldridge14.html

and in the Example 14.2: Has the Return to Education Changed Over Time, Kit Baum used Stata command as such:

xtreg lwage expersq union married d81-d87 edd81-edd87, fe

This command gives coefficient of -.0157891 on variable edd87, with t= -1.14, while in Wooldridge's textbook(page 488), the coefficient of variable edd87 is 0.030, and its t-value is 2.48. And according to descriptions in the textbook, coefficients and t-value on the remaining variables are all inconsistent between Baum and Wooldridge.
I wonder if there were something I missed or I misunderstand the statistical procedure.
Would anybody give me some advice?

[William Lisowski]

Wooldridge writes

We use log(wage) as the dependent variable, dummy variables for marital and union status, a full set of year dummies, and the interaction terms d81*educ, d82*educ, ..., d87*educ.

However, the model you quote from Kit Baum also includes expersq - apparently, the square of experience. Leaving that out of the regression produces results that are, at first glance, consistent with what you report from Wooldridge. I will note that the web page you cite was last revised in 2002 (per the note at the bottom) and reflects the 1st and 2nd editions (per the note at the top).

.  xtreg lwage /* expersq */ union married d81-d87 edd81-edd87, fe

Fixed-effects (within) regression               Number of obs     =      4,360
Group variable: nr                              Number of groups  =        545

R-sq:                                           Obs per group:
     within  = 0.1708                                         min =          8
     between = 0.1900                                         avg =        8.0
     overall = 0.1325                                         max =          8

                                                F(16,3799)        =      48.91
corr(u_i, Xb)  = 0.0991                         Prob > F          =     0.0000

------------------------------------------------------------------------------
       lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       union |   .0829785   .0194461     4.27   0.000     .0448527    .1211042
     married |   .0548205   .0184126     2.98   0.003      .018721      .09092
         d81 |  -.0224159   .1458885    -0.15   0.878    -.3084432    .2636114
         d82 |  -.0057613   .1458558    -0.04   0.968    -.2917245    .2802019
         d83 |   .0104296   .1458579     0.07   0.943    -.2755378     .296397
         d84 |   .0843743   .1458518     0.58   0.563    -.2015812    .3703297
         d85 |   .0497251   .1458602     0.34   0.733    -.2362467    .3356969
         d86 |   .0656064   .1458917     0.45   0.653    -.2204273    .3516401
         d87 |   .0904447   .1458505     0.62   0.535    -.1955082    .3763976
       edd81 |   .0115854   .0122625     0.94   0.345    -.0124562    .0356271
       edd82 |   .0147905   .0122635     1.21   0.228    -.0092532    .0388342
       edd83 |   .0171182   .0122633     1.40   0.163    -.0069251    .0411615
       edd84 |   .0165839   .0122657     1.35   0.176     -.007464    .0406319
       edd85 |   .0237086   .0122738     1.93   0.053    -.0003554    .0477725
       edd86 |   .0274123    .012274     2.23   0.026     .0033481    .0514765
       edd87 |   .0304332   .0122723     2.48   0.013     .0063722    .0544942
       _cons |   1.362459   .0162385    83.90   0.000     1.330622    1.394296
-------------+----------------------------------------------------------------
     sigma_u |  .37264192
     sigma_e |  .35335714
         rho |  .52654437   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(544, 3799) = 8.09                   Prob > F = 0.0000

[Chen Samulsion]

William Lisowski, thank you very much. You are right, in the fifth editon, Wooldridge modify its equation, droping the variable 'expersq' (i.e. exper^2).

[2nd Edition:]We use log(wage) as the dependent variable, a quadratic in experience, dummy variables for marital and union status, a full set of year dummies, and the interaction terms d81*educ, d82*educ, …, d87*educ.

[5th Edition:]We use log(wage) as the dependent variable, dummy variables for marital and union status, a full set of year dummies, and the interaction terms d81*educ, d82*educ, ..., d87*educ.

Nevertheless, the 2nd edition gives same results (The largest coefficient of .030 is on d87educ, with t = 2.48) as the 5th edition, so I think this was a mistake in 2nd edition and was corrected in 5th editon.
Thank you again Mr. Lisowski and best wishes.

[William Lisowski]

I suspect Wooldridge may have initially intended to make the point that while exper (experience) cannot be used because it increases by 1 year each year, and thus is collinear with the collection of time effects in less-obvious way (it took me a while to work out what was happening), its square does not suffer from collinearity. And then he wisely decided not to make that subtle point, and removed expersq from the model he ran whose results he quoted, but overlooked removing it from the description of the model. Thank you for closing the loop.

[Chen Samulsion]

In lines before sentences that we quoted, Wooldridge indeed made statement about collinearity of exper & expersq. I think that what you wrote in #4 is close to the truth.