Re: st: fixed, random effects

 From "Clive Nicholas" To statalist@hsphsun2.harvard.edu Subject Re: st: fixed, random effects Date Mon, 28 Nov 2005 01:37:02 -0000 (GMT)

Raphael Schoenle wrote:

> I have tried to solve a simple problem for days but I can't figure out
> how to run it properly in Stata. If someone could give me a hint, this
> would be really great.
>
> Basically, I want to run a standard fixed, and random effects
> regression (xtreg in STATA) but with _variable_ weights (they
> correspond to changing industry shares in the market).
>
> So, for the random effects I tried gllamm but always get an error
> message of insufficient observations when I try to use weights.
>
> Here is what I do:
>
> sort ind7090
> gllamm dsc dperc dcomp, i(ind7090) pw(wt)
>
> any ideas what goes wrong?
>
> (if there are no weights, then we just get the xtreg dsc dperc dcomp,
> fe results.)

One elementary solution that gets round this problem in -gllamm- (or
-xtreg-, if you prefer) would be to interact your weight with each of the
explanatory variables in your model. However, the specification I would
offer you might prove controversial to some in terms of model
specification and thus model interpretation (see below).

First, using a toy dataset, let's generate some weights and interactions
(when you run this, notice how carefully I've simulated the weighting
variable here):

. clear

. webuse grunfeld

. g weight=invnorm(uniform())

. replace weight=(weight+_N)/_N

. g mvalueXweight=mvalue*weight

. g kstockXweight=kstock*weight

. g timeXweight=time*weight

. tsset company year

. gllamm invest mvalue kstock time, i(company)

Iteration 0:   log likelihood = -1191.6318  (not concave)

[...]

Iteration 7:   log likelihood = -1098.0719

number of level 1 units = 200
number of level 2 units = 10

Condition Number = 3885.5639

gllamm model

log likelihood = -1098.0719

Robust standard errors
--------------------------------------------------------------------------
invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------+----------------------------------------------------------------
mvalue |   .1096954    .005726    19.16   0.000     .0984726    .1209182
kstock |   .3745101   .0342796    10.93   0.000     .3073233     .441697
time |  -3.206458   1.828845    -1.75   0.080    -6.790929    .3780136
_cons |  -42.40668   18.85687    -2.25   0.025    -79.36547   -5.447888
---------------------------------------------------------------------------

Variance at level 1
---------------------------------------------------------------------------

3044.6811 (1075.4094)

Variances and covariances of random effects
---------------------------------------------------------------------------

***level 2 (company)

var(1): 9104.3989 (1377.012)
---------------------------------------------------------------------------

Note the coefficients you see here compared what is to come. Now, we run
the 'interactive' model with weights:

. gllamm invest mvalueXweight kstockXweight timeXweight, i(company)

Iteration 0:   log likelihood = -1191.2958  (not concave)

[...]

Iteration 7:   log likelihood = -1097.8643

number of level 1 units = 200
number of level 2 units = 10

Condition Number = 3887.1525

gllamm model

log likelihood = -1097.8643

---------------------------------------------------------------------------
invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------+----------------------------------------------------------------
mvalueXwe |   .1096633   .0035387    30.99   0.000     .1027276     .116599
kstockXwe |    .374551    .019511    19.20   0.000     .3363102    .4127917
timeXwe |  -3.184235   .8377363    -3.80   0.000    -4.826168   -1.542302
_cons |  -42.58643   8.758511    -4.86   0.000     -59.7528   -25.42007
---------------------------------------------------------------------------

Variance at level 1
---------------------------------------------------------------------------

3038.3736 (303.91209)

Variances and covariances of random effects
---------------------------------------------------------------------------

***level 2 (company)

var(1): 9065.5516 (936.56468)
---------------------------------------------------------------------------

The parameter estimates, their standard errors, the overall model fit and
the model diagnostics barely change. That's how it should be: the weight
is only deployed to make slight upward or downward adjustments on the
estimates. The parameter estimates don't change at all if I add -year- as
the level 1 variable (i.e, -i(year company)-, although it comes out as a
level 2 variable! Still estimating the variable at this level turns out to
produce some interesting information).

Note here that I do not follow the model specification as advised by
Braumoeller (2004) when running models with interactions. He argues that
you _must_ include the first order terms and the interaction variable
(here, the weight) along with the interaction terms. However, running this
'full' model here forces us to interpret the interaction coefficients
only, but you will find that if you do this, all of the coefficient signs
are (implausibly) reversed. Interpretation on the first-order terms (i.e.,
the original variables) is inadmissible in this model because the
coefficients only take these values when the weight = 0: but none of the
weights are 0 in our example. You'll also get some ridiculously large
coefficients in the 'full' model as well.

Thus, I would argue that, in this instance, it would be more sensible to
run the pared-down 'interactive' model I've shown here.

I hope this helps. :)

CLIVE NICHOLAS        |t: 0(044)7903 397793
Politics              |e: clive.nicholas@ncl.ac.uk
Newcastle University  |http://www.ncl.ac.uk/geps

Reference:

Braumoeller BF (2004) "Hypothesis Testing and Multiplicative Interaction
Terms", INTERNATIONAL ORGANIZATION 58(4): 807-20.

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