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st: Interaction terms in fixed effects analysis


From   tara.iyer@duke.edu
To   statalist@hsphsun2.harvard.edu
Subject   st: Interaction terms in fixed effects analysis
Date   Sat, 7 Feb 2009 23:44:27 -0500

Hi,

I'm using panel data to analyze the effect of educational expenditure per
student on test scores across 100 Indian districts over two years. Now, these
100 districts belong to three different states. To capture the different effect
of expenditure on test scores across the three states, I used the *xi* command
to interact *perstudent* and *state*, with state as the group variable. I'm
using both OLS and Fixed Effects regression (the OLS regression table is
below). However, I'm not quite sure how to interpret the regression
coefficients. I have three specific questions:

1. In OLS, is the effect of expenditure in State 2 on *testscore* 11.16 units
more than State 1? Or is it 11.16 - 0.0068 (-0.0068 is the coefficient on the
interaction between state 2 and expenditure)

2. In Fixed Effects, _Istate_2 and _Istate_3 were dropped. _IstaXpers~2 and
_IstaXpers~3 were not. How would one interpret the coefficients on IstaXpers~2
and _IstaXpers~3 in the Fixed Effects model?

3. Does the coefficient on *perstudent* indicate that increasing expenditure
across *all three states*  is decreasing testscores by 0.0025 units? Or does
*perstudent* refer to a specific state?

Thank you. I really appreciate your taking the time to help.

Regards,
Tara Iyer

. xi: reg testscore i.state*perstudent

i.state           _Istate_1-3         (naturally coded; _Istate_1 omitted)
i.state*perst~t   _IstaXperst_#       (coded as above)

      Source |       SS       df       MS              Number of obs =     230
-------------+------------------------------           F(  5,   224) =   22.51
       Model |  15291.7444     5  3058.34888           Prob > F      =  0.0000
    Residual |  30436.1777   224  135.875793           R-squared     =  0.3344
-------------+------------------------------           Adj R-squared =  0.3196
       Total |  45727.9221   229  199.685249           Root MSE      =  11.657

------------------------------------------------------------------------------
         ner |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   _Istate_2 |   11.15724   7.264148     1.54   0.126    -3.157571    25.47205
   _Istate_3 |   10.23105   6.075904     1.68   0.094    -1.742197    22.20429
  perstudent |  -.0024748   .0013051    -1.90   0.059    -.0050468    .0000971
_IstaXpers~2 |  -.0067742   .0022988    -2.95   0.004    -.0113042   -.0022441
_IstaXpers~3 |  -.0020089   .0016681    -1.20   0.230    -.0052961    .0012783
       _cons |   97.34217   2.719425    35.80   0.000     91.98324    102.7011

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