Difference between coefficients from xtlogit,fe and xthybrid

[Emma Maun]

I am using xtlogit, fe with panel data, but I also want to consider the average effect for different groups, so also run xthybrid to get "between" coefficients. In one of my models I have got quite different "within" coefficients from xtlogit, fe and xthybrid. I am not sure why and whether something is not working well. I am using Stata 15.1 for Windows.

I have three waves of panel data and am doing gender-stratified analyses on 4.5k women and 3.6k men. My dependent variable is binary so I'm using xtlogit, fe (as Hausman test of diff in coefficients, fe:re was significant), and as I am interested in the average effect of being in certain categories of my main explanatory variable, I am comparing to coefficients from xthybrid, to compare change within individuals and on average for my coefficient of interest. I am using both types of model as the Stata journal article discussing xthybrid highlights there may be slight differences in the "within" coefficients produced by xthybrid due to the method

of estimating, and recommends comparing with xtlogit, fe. In most of my models the xtlogit, fe and xthybrid coefficients match fairly well, but in one of my models the difference in coefficients produced by xtlogit,fe and xthybrid is large - 20% - for some variables, though the direction is the same. I am not sure why the difference might be so large and what might be the reason. The Stata article is

Schunck, R. and Perales, F., 2017. Stata Journal, 17(1), pp. 89-115 (p112 discusses differences in coefficients).

I am most interested in the difference in coefficients for one category from the main explanatory variable, hrcaredum3 - fe coefficient compared to the W__hrcaredum3 coefficient from xthybrid, comparison table below (though other variables also differ).

estimates table  fe whybrid,  /// 
 b(%6.4f) stfmt(%6.0g)se keep(hrcaredum3 W__hrcaredum3 B__hrcaredum3 depcesd3_NS W__depcesd3_NS B__depcesd3_NS) stats(sigma_u N N_g g_avg)

----------------------------------
    Variable |   fe      whybrid 
-------------+--------------------
  hrcaredum3 |  0.4069           
             |  0.2212           
W__hrcared~3 |            0.4813 
             |            0.2152 
B__hrcared~3 |            0.8993 
             |            0.3261 
 depcesd3_NS |  0.6798           
             |  0.1070           
W__depcesd~S |            0.7358 
             |            0.1083 
B__depcesd~S |            2.1250 
             |            0.1689 
-------------+--------------------
     sigma_u |                   
           N |    3440     11782 
         N_g |    1276           
       g_avg |   2.696           
----------------------------------
                      legend: b/se

The coefficients come from the models run below:

Xtlogit, fe command and output below

xtlogit slp_qual_bin hrcaredum2 hrcaredum3 indager indager_sq wavedum2 wavedum3 multi_role_bin workcat maritaldum2 maritaldum3 nh_wealthdum2-nh_wealthdum5 modvig_act lim_illdum2 lim_illdum3 pain healthstat depcesd3_NS if indsex==1, fe
est store fe

Xthybrid code and output

xthybrid slp_qual_bin hrcaredum2 hrcaredum3 indager indager_sq wavedum2 wavedum3 multi_role_bin workcat maritaldum2 maritaldum3 nh_wealthdum2-nh_wealthdum5 modvig_act lim_illdum2 lim_illdum3 pain healthstat depcesd3_NS if indsex==1, clusterid(idauniq) family(binomial) link(logit) test full
est store whybrid

Thanks very much in advance for any help.