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# st: RE: Find the mean of observations from a variable that satisfy a condition in another variable

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: Find the mean of observations from a variable that satisfy a condition in another variable Date Fri, 12 Aug 2011 18:12:03 +0100

```A stretched analogue is

. sysuse auto, clear
(1978 Automobile Data)

. ttest mpg if rep78 == 4 | rep78 == 5, by(rep78)

Two-sample t test with equal variances
------------------------------------------------------------------------------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
4 |      18    21.66667     1.16316     4.93487    19.21261    24.12072
5 |      11    27.36364    2.632913    8.732385    21.49714    33.23013
---------+--------------------------------------------------------------------
combined |      29    23.82759    1.312191    7.066364    21.13969    26.51549
---------+--------------------------------------------------------------------
diff |            -5.69697    2.526323               -10.88056   -.5133831
------------------------------------------------------------------------------
diff = mean(4) - mean(5)                                      t =  -2.2550
Ho: diff = 0                                     degrees of freedom =       27

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.0162         Pr(|T| > |t|) = 0.0324          Pr(T > t) = 0.9838

Here there are two simple but useful tricks

1. The -if- condition ensures precisely two groups are looked at.

2. The -by()- option ensures a comparison between those groups.

In your case, you should probably want to do something similar but with -xtreg-. Quite what different dependence assumptions apply with panel data is something to think about.

N.B. A standard -ttest- can be done using -regress-: e.g.

. gen mygroup = rep78 - 4 if rep78 > 3
(45 missing values generated)

. regress mpg mygroup

Source |       SS       df       MS              Number of obs =      29
-------------+------------------------------           F(  1,    27) =    5.09
Model |  221.592476     1  221.592476           Prob > F      =  0.0324
Residual |  1176.54545    27  43.5757576           R-squared     =  0.1585
-------------+------------------------------           Adj R-squared =  0.1273
Total |  1398.13793    28  49.9334975           Root MSE      =  6.6012

------------------------------------------------------------------------------
mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mygroup |    5.69697   2.526323     2.26   0.032     .5133831    10.88056
_cons |   21.66667   1.555916    13.93   0.000     18.47419    24.85914
------------------------------------------------------------------------------

. replace mygroup = -mygroup
(11 real changes made)

. regress mpg mygroup

Source |       SS       df       MS              Number of obs =      29
-------------+------------------------------           F(  1,    27) =    5.09
Model |  221.592476     1  221.592476           Prob > F      =  0.0324
Residual |  1176.54545    27  43.5757576           R-squared     =  0.1585
-------------+------------------------------           Adj R-squared =  0.1273
Total |  1398.13793    28  49.9334975           Root MSE      =  6.6012

------------------------------------------------------------------------------
mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mygroup |   -5.69697   2.526323    -2.26   0.032    -10.88056   -.5133831
_cons |   21.66667   1.555916    13.93   0.000     18.47419    24.85914
------------------------------------------------------------------------------

All that said, you want to do comparisons between three times, and quite what the underlying generating process is will determine the appropriate model to fit. I don't know what you know about equity issuance, and I can't advise.

Nick
n.j.cox@durham.ac.uk