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# st: Fixed effects

 From Mohamud Hussein To "statalist@hsphsun2.harvard.edu" Subject st: Fixed effects Date Wed, 6 Feb 2013 18:58:45 +0000

```Dear All,

I got in touch this morning to ask help on the problem below, but was later on informed that some of my notations(Greek alphabets) where unreadable, so I re-submit the problem:

I would like to compare the cost-effectiveness of a regulatory regime used for inspections for two distinct groups of (small and large) firms. I intend to use a dummy (i.g287) coding for the (output) size of a firm and then compare two groups on the basis of differences in the intercepts and coefficients.

Cit = mi + (beta)xit + zit(gamma) + nt + (epsilon)it.

C= total cost of the inspection regime

m=constant

x= cost of the regime per unit of output

z= Y_TCOST10, agr_score10 and enforcement10 (i.e. a set of other variables related to regulatory performance of a firm)
n= dummy intercept(i.e. for i.g287). This is time-variant , allowing a firm to grow its operation from small to large scale in time.
epsilon= error term

I also added interactions with the dummy and run the model with intention of estimating directly both the coefficients for the group (dummy=0) and coefficients for the difference between the two groups. Output of the model (see below) suggest that there is no significant difference in the intercepts, but there is a significant difference in the coefficients for x and agr_score10.

I am not quite sure of whether model is suitable for the comparison I am trying to make and, if so how to interpret the results? In particular, how I should interpret the insignificant difference in the intercepts and highly significant coefficients on interactions terms for variables x and agr_score10, bearing in mind that the dummy represent the size of a firm in a group in this case?

Also, any particular issues that I need to pay an attention, if the model is does what I want?

I will be happy to provide any additional information or explanation that may be necessary.

. xtreg  C  i.gt287##c.x i.gt287##c.Y_TCOST10  i.gt287##c.agr_score10 i.gt287##c.enforcement10, fe

Fixed-effects (within) regression               Number of obs      =       474
Group variable: my_id                           Number of groups   =        94

R-sq:  within  = 0.5648                         Obs per group: min =         1
between = 0.9508                                        avg =       5.0
overall = 0.9316                                        max =         8

F(9,371)           =     53.50
corr(u_i, Xb)  = 0.3923                         Prob > F           =    0.0000

---------------------------------------------------------------------------------------
C	    |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
1.gt287 |  -34127.98   24120.31    -1.41   0.158    -81557.65    13301.69
x   |   .0066293   .0078059     0.85   0.396    -.0087201    .0219787
|
gt287#c.x   |
|   .4754795   .1637735     2.90   0.004     .1534387    .7975203
|
Y_TCOST10 |   .3695438    .502372     0.74   0.462    -.6183098    1.357398
|
gt287#c.Y_TCOST10 |
1  |  -.2244589   .5022651    -0.45   0.655    -1.212102    .7631844
|
agr_score10 |  -16.97173   18.80148    -0.90   0.367    -53.94256    19.99909
|
gt287#c.agr_score10 |
1  |   109.7228   23.18021     4.73   0.000     64.14173    155.3039
|
enforcement10 |  -1.241843   31.77901    -0.04   0.969    -63.73141    61.24773
|
gt287#c.enforcement10 |
1  |  -7.497396   33.53713    -0.22   0.823     -73.4441    58.44931
|
_m    |   37718.32   19743.62     1.91   0.057    -1105.108    76541.75
----------------------+----------------------------------------------------------------
sigma_u |  33442.826
sigma_e |  30638.016
rho |  .54368618   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------
F test that all u_i=0:     F(93, 371) =     4.62             Prob > F = 0.0000

Thanks,
Mohamud

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```