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# Re: st: How do I test whether the time path of income differs between two groups?

 From andreas nordset To statalist@hsphsun2.harvard.edu Subject Re: st: How do I test whether the time path of income differs between two groups? Date Mon, 29 Nov 2010 11:50:26 +0100

```Thank you Marten! That way of testing does actually make much more sense now.

As I read you reply, I just realized one further point though which I

The income time paths of the two groups will differ for two reasons:
Firstly group 1 has higher average income than group 2, and secondly
group 1 experiences a stronger drop, in percentage terms, from, let's
say, relative year -2 to relative year 0. Now in fact I would like to
test only whether the drop is significantly different, not whether the
levels are. If I do the F test on all interaction terms, then I will
presumably also get a high test statistic and hence reject the Null of
no difference if the time paths are exactly identical, but are just
sufficiently parallelly shifted.

Restricting it for simplicity for now to a test of whether the
percentage drops between relative year -2 and 0 differ, I think the
difference I would want to compute is this, where pinc is predicted
income, RY stands for relative year and the groups are G1 and G2:
{ [pinc(RY=-2,G1) - pinc(RY=0,G1) ] / pinc(RY=-2,G1) } -  {
[pinc(RY=-2,G2) - pinc(RY=0,G2) ] / pinc(RY=-2,G2) }

I am however not sure what the standard error of this more complex
term would be, given the division to get a percentage change. I'm
thinking that maybe I could get that of the first term alone by
predicting incomes after the regression, then summarizing for the
relevant group, and then taking the SD and dividing by sqrt(N). Then
do the same for the second term, and then pool the two SEs as
SE_pooled = sqrt(SE1^2 + SE2^2)?
Then to jointly test that the percentage changes between relative year
-2 and each of the other relative years is the same, I would have to
do some sort of F test along these lines? Or is there a more
straightforward way of doing this?

Many thanks,
Andreas

On Mon, Nov 29, 2010 at 10:55 AM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- On Mon, 29/11/10, andreas nordset wrote:
>> So I am regressing income on a set of "relative year"
>> dummies to capture how it develops around an event.
>> Furthermore, I would like to estimate two separate time
>> paths for two separate groups, so I run:
>> - reg inc (ry_m2 ry ry_m1 ry_0 ry_p1 ry_p2) (iry_m2 iry
>> iry_m1 iry_0 iry_p1 iry_p2) -
>> where the second set of dummies is the first one interacted
>> with the dummy for membership of the second group.
> <snip>
>> Now here's the question: How do I appropriately test
>> whether the time paths of the two groups are significantly
>> different? I suppose that in any specific relative year
>> they are if the two confidence intervals do not overlap,
>> but how can I do a joint test for all relative
>> years?
>
> No, looking whether confidence intervals overlap is not a
> test of the hypothesis that the coeficients are equal. That
> way you are ignoring the covariance in the sampling
> distribution of both estimates.
>
> Instead I would estimate all in one model with interaction
> terms, and than test whether all interaction terms are
> equal to 0. This is probably easiest using Stata's factor
> variable notation:
>
> *---------------------- begin example ---------------------
> sysuse auto, clear
> recode rep78 1/2=3
>
> // estimate the model with interaction terms
> reg price i.rep78##i.foreign
>
> // see how Stata stores the coeficients
> reg, coefl
>
> test  _b[4.rep78#1.foreign] = _b[5.rep78#1.foreign] = 0
> *----------------- end example ---------------------------
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> --------------------------
>
>
>
>
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```