Variables	Separate	Cmp on	Cmp with	Our method
	equations	pooled data	random effects	xtcmp
Binary outcome: ${\tilde{y}}_{i t}^{1}$
x1	$\underset{(0.0166)}{0.0238}$	$\underset{(0.0062)}{- 0.0056}$	$\underset{(0.0224)}{0.0021}$	$\underset{(0.0082)}{0.0119}$
x2	$\underset{(0.0238)}{{0.2569}^{***}}$	$\underset{(0.0034)}{{0.0297}^{***}}$	$\underset{(0.0045)}{{0.0484}^{***}}$	$\underset{(0.0037)}{{0.0204}^{***}}$
x3	$\underset{(0.1228)}{{0.3171}^{**}}$	$\underset{(0.006)}{0.0053}$	$\underset{(0.0224)}{0.0351}$	$\underset{(0.0265)}{0.0254}$
x4	$\underset{(0.2182)}{- {0.5748}^{***}}$	$\underset{(0.0112)}{- 0.0084}$	$\underset{(0.0399)}{- 0.058}$	$\underset{(0.0471)}{- 0.0463}$
Intercept	$\underset{(0.375)}{- {6.4382}^{***}}$	$\underset{(0.0379)}{- {0.7083}^{***}}$	$\underset{(0.1339)}{{1.1074}^{***}}$	$\underset{(0.0535)}{- {2.7151}^{***}}$
Continuous outcome: ${\tilde{y}}_{i t}^{3}$
x7	$\underset{(0.0207)}{- {0.1528}^{***}}$	$\underset{(0.0168)}{- {0.0321}^{*}}$	$\underset{(0.015)}{- {0.1044}^{***}}$	$\underset{(0.0158)}{- {0.0422}^{***}}$
x9	$\underset{(0.004)}{{0.0384}^{***}}$	$\underset{(0.0047)}{{0.1035}^{***}}$	$\underset{(0.004)}{{0.0361}^{***}}$	$\underset{(0.0043)}{{0.096}^{***}}$
Intercept	$\underset{(0.7339)}{{15.9964}^{***}}$	$\underset{(0.5086)}{{10.0568}^{***}}$	$\underset{(0.4477)}{{17.0243}^{***}}$	$\underset{(0.4779)}{{7.4308}^{***}}$
Covariance matrix: individual effects
$σ_{1}$	$\underset{(0.2135)}{{3.8635}^{***}}$	-	$\underset{(0.2144)}{{2.8431}^{***}}$	$\underset{(0.1263)}{{2.0702}^{***}}$
$σ_{2}$	6.024	-	$\underset{(0.1789)}{{5.706}^{***}}$	$\underset{(0.1421)}{{2.2481}^{***}}$
$ρ_{1}$	-	-	$\underset{(0.0247)}{{0.5135}^{***}}$	$\underset{(0.0417)}{{0.8196}^{***}}$
Covariance matrix: idiosyncratic errors
$σ$	2.6596	$\underset{(0.1172)}{{6.7719}^{***}}$	$\underset{(0.0481)}{{2.6725}^{***}}$	$\underset{(0.1182)}{{6.472}^{***}}$
$ρ$	-	$\underset{(0.0349)}{{0.1525}^{***}}$	$\underset{(0.0528)}{0.0342}$	$\underset{(0.0418)}{{0.5087}^{***}}$