st: FW: Fixed effects

[Mohamud Hussein <Mohamud.Hussein@fera.gsi.gov.uk>]

On Nick Cox's advice (thanks), I have reformatted the email as plain text and add details to the reference as below.

-----Original Message-----
From: Mohamud Hussein 
Sent: 06 February 2013 10:27
To: 'statalist@hsphsun2.harvard.edu'
Subject: FW: Fixed effects

Sorry all, I should have added the specification of model that I run:

Cit =αi+ βxit + zitγ + δt + εit.


αi=intercept

δi = dummy intercept.

The basic model is described in Greene, William, H. (2008): Econometric Analysis, 6th Ed., page 197, Pearson, New Jersay; but I added interactions and implemented it such that I can run it to estimate directly the coefficients for the first group (dummy=0) and difference between the two groups on interaction between a variable and the dummy. In this setting, I think, the coefficient on P_O is  0.0066293 for group with dummy (1.gt287) =0 , and 0.0066293+0.4754795 for group with dummy=1.

I would be grateful if you can tell me:
1.  whether I implemented the model correctly;
 
2. and what the insignificant difference between intercepts(α and δ) and highly significant difference between the coefficients for variables x and agr_score10 mean, bearing in mind that the dummy intercept represent the size of the firm in this case? 

I also welcome any general comment on the results.

For description of the problem, dummy set up and full model output see my previous email below. Note that z= Y_TCOST10, agr_score10 and enforcement10.

Thanks,
Mohamud

-----Original Message-----
From: Mohamud Hussein 
Sent: 05 February 2013 16:41
To: 'statalist@hsphsun2.harvard.edu'
Subject: Fixed effects

Hi there,

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

I run a fixed effects model and obtained the results below (second model) which suggest there no significant difference in the intercepts but two of the coefficients for interactions of the dummy and the variables in the model are highly significant. I am mostly interested in establishing whether difference between the firms is due to size-related heterogeneity and hence used the interactions between the dummy for size and other variables in this case.

I am not quite sure of how to interpret the results? Can someone please help me with this. 

Also, I welcome any general comments on the results.

Thanks,
Mohamud
------------------

gen gt287 = 1 if subsector=="PSL" & pia_costs>0 & output>287000
(4970 missing values generated)

. 
. replace gt287 = 0 if subsector=="PSL" & pia_costs>0 & output<=287000
(163 real changes made)

. 
. xtreg  TCOST  i.gt287##c.P_O 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

---------------------------------------------------------------------------------------
                TCOST |      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
                      |
                _cons |   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

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