Hi all,

I am trying to calculate confidence intervals for the difference of two regression coefficient means.

I have panel data on mututal fund flows, performance and market states and I am running two types of quarterly cross sectional regressions:
- reg flows low_performance
- reg flows high_performance
where low and high performance are just the performance variable split in two.

Then I store the coefficients ( FPS_L and FPS_H ) of each regression and each quarter and average them according to the market states variable (total of 10 market states), which gives me the average flow performance sensitivity of low performance (avg_FPS_L) and high performance (avg_FPS_H) in each market state (group_mkt_rf). Then I managed to calculate the confidence intervals of those averages within each market state using ci mean.


What I am interested in is the difference in sensitivity to low and high performance in each market state, so for each market state I subtract the average sensitivity to high performance from the average sensitivity to low performance. And what I want to calculate next is the confidence interval for this difference.


I tried the following approaches which give me the same result, but I am unsure whether this is the correct result at all. So I would much appreciate some guidance on whether my approach makes (statistical) sense.


Examples for market state 1:

1)
Code:
// generate difference between sensitivity to low and high performance
gen FPS_LH = FPS_L - FPS_H
// calculate CI for mean of differences for market state 1
ci mean FPS_LH if group_mkt_rf==1
Output:
Code:
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
      FPS_LH |          8    .2283137    .3054095        -.493865    .9504923

2)
Code:
ttest FPS_L ==FPS_H if  group_mkt_rf==1
Code:
Paired t test
------------------------------------------------------------------------------
Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
   FPS_L |       8   -.1396271    .3490874    .9873682   -.9650876    .6858334
   FPS_H |       8   -.3679408    .4586592    1.297284   -1.452497    .7166158
---------+--------------------------------------------------------------------
    diff |       8    .2283137    .3054095    .8638284    -.493865    .9504923
------------------------------------------------------------------------------
     mean(diff) = mean(FPS_L - FPS_H)                             t =   0.7476
 Ho: mean(diff) = 0                              degrees of freedom =        7

 Ha: mean(diff) < 0           Ha: mean(diff) != 0           Ha: mean(diff) > 0
 Pr(T < t) = 0.7605         Pr(|T| > |t|) = 0.4791          Pr(T > t) = 0.2395