Variables	Separate	Cmp on	Our method
	equations	pooled data	xtcmp
Binary outcome 1: ${\tilde{y}}_{i t}^{1}$
x1	$\underset{(0.0166)}{0.0238}$	$\underset{(0.0063)}{- 0.0067}$	$\underset{(0.0146)}{{0.0399}^{***}}$
x2	$\underset{(0.0238)}{{0.2569}^{***}}$	$\underset{(0.0034)}{{0.0326}^{***}}$	$\underset{(0.0042)}{{0.2313}^{***}}$
x3	$\underset{(0.1228)}{{0.3171}^{**}}$	$\underset{(0.0072)}{0.0065}$	$\underset{(0.0379)}{0.0445}$
x4	$\underset{(0.2182)}{- {0.5748}^{***}}$	$\underset{(0.0132)}{- 0.0107}$	$\underset{(0.0669)}{- 0.0826}$
Intercept	$\underset{(0.375)}{- {6.4382}^{***}}$	$\underset{(0.0379)}{- {0.7176}^{***}}$	$\underset{(0.1247)}{- {2.7205}^{***}}$
Binary outcome 2: ${\tilde{y}}_{i t}^{2}$
x4	$\underset{(0.0480)}{{0.1678}^{***}}$	$\underset{(0.0078)}{0.0076}$	$\underset{(0.0584)}{{0.1345}^{**}}$
x6	$\underset{(0.0136)}{- {0.1068}^{***}}$	$\underset{(0.0031)}{- {0.0499}^{***}}$	$\underset{(0.0041)}{- {0.0201}^{***}}$
x7	$\underset{(0.0193)}{- {0.0812}^{***}}$	$\underset{(0.0040)}{- {0.0418}^{***}}$	$\underset{(0.0071)}{- {0.0230}^{***}}$
Intercept	$\underset{(1.0978)}{{8.8666}^{***}}$	$\underset{(0.2625)}{{4.2916}^{***}}$	$\underset{(0.3885)}{{1.8381}^{***}}$
Continuous outcome: ${\tilde{y}}_{i t}^{3}$
x7	$\underset{(0.0207)}{- {0.1528}^{***}}$	$\underset{(0.0168)}{- {0.0343}^{*}}$	$\underset{(0.0123)}{- {0.0643}^{***}}$
x9	$\underset{(0.004)}{{0.0384}^{***}}$	$\underset{(0.0049)}{{0.1005}^{***}}$	$\underset{(0.0034)}{{0.0608}^{***}}$
Intercept	$\underset{(0.7339)}{{15.9964}^{***}}$	$\underset{(0.5172)}{{10.2621}^{***}}$	$\underset{(0.3771)}{{12.4296}^{***}}$
Covariance matrix: individual effects
$σ_{1}$	$\underset{(0.2135)}{{3.8635}^{***}}$	-	$\underset{(1.518)}{{24.123}^{***}}$
$σ_{2}$	$\underset{(0.3417)}{{3.0296}^{***}}$	-	$\underset{(0.485)}{{6.5402}^{***}}$
$σ_{3}$	6.024	-	$\underset{(0.235)}{{3.7135}^{***}}$
$ρ_{1,2}$	-	-	$\underset{(0.0853)}{{0.2091}^{**}}$
$ρ_{1,3}$	-	-	$\underset{(0.0854)}{{0.2379}^{***}}$
$ρ_{2,3}$	-	-	$\underset{(0.0565)}{{0.6346}^{***}}$
Covariance matrix: idiosyncratic errors
$σ$	2.6596	$\underset{(0.1175)}{{6.7756}^{***}}$	$\underset{(0.0870)}{{4.6060}^{***}}$
$ρ_{1}$	-	$\underset{(0.0464)}{{0.2468}^{***}}$	$\underset{(0.0681)}{{0.8719}^{***}}$
$ρ_{2}$	-	$\underset{(0.0404)}{{0.1132}^{***}}$	$\underset{(0.0274)}{{0.8631}^{***}}$
$ρ_{3}$	-	$\underset{(0.0354)}{{0.1501}^{***}}$	$\underset{(0.0565)}{{0.5906}^{***}}$