Equation (1) Equation (2) DGP coef: coef: DGP coef: coef: (1) (2) (3) (1’) (2’) (3’) Dynamic Equation y1 − 1 0.3 $\underset{\left(0.05\right)}{{0.2195}^{***}}$ $\underset{\left(0.05\right)}{{0.2184}^{***}}$ −0.1 $\underset{\left(0.0567\right)}{-0.0051}$ $\underset{\left(0.0568\right)}{-0.0052}$ y2 − 1 0.1 $\underset{\left(0.0513\right)}{{0.1267}^{**}}$ $\underset{\left(0.0513\right)}{{0.1283}^{**}}$ 0.4 $\underset{\left(0.061\right)}{{0.4926}^{***}}$ $\underset{\left(0.0612\right)}{{0.4944}^{***}}$ Gender = Male −0.05 $\underset{\left(0.0521\right)}{-0.0554}$ $\underset{\left(0.0521\right)}{-0.0571}$ 0.05 $\underset{\left(0.0594\right)}{0.073}$ $\underset{\left(0.0596\right)}{0.0751}$ Medical density − − − 0.5 $\underset{\left(1.1111\right)}{0.5687}$ $\underset{\left(1.1112\right)}{0.5567}$ Unemployment rate −0.2 $\underset{\left(0.0269\right)}{-{0.1682}^{***}}$ $\underset{\left(0.0269\right)}{-{0.1698}^{***}}$ − − − Not French − − $\underset{\left(0.0956\right)}{0.1246}$ − − $\underset{\left(0.1076\right)}{0.0015}$ rural − − $\underset{\left(0.0628\right)}{0.0743}$ − − $\underset{\left(0.0719\right)}{0.0283}$ Intercept 1.9 $\underset{\left(0.2667\right)}{{2.3113}^{***}}$ $\underset{\left(0.2667\right)}{{2.2994}^{***}}$ −0.04 $\underset{\left(2.122\right)}{-0.4677}$ $\underset{\left(2.1215\right)}{-0.4527}$ Initial Conditions Illness before prof: life 0.3 $\underset{\left(0.0283\right)}{{0.3032}^{***}}$ $\underset{\left(0.0283\right)}{{0.3032}^{***}}$ −0.2 $\underset{\left(0.0221\right)}{-{0.1624}^{***}}$ $\underset{\left(0.0221\right)}{-{0.1627}^{***}}$ Age − − − −0.08 $\underset{\left(0.0202\right)}{-{0.093}^{***}}$ $\underset{\left(0.0202\right)}{-{0.0932}^{***}}$ Unemployment rate −0.2 $\underset{\left(0.057\right)}{-{0.144}^{**}}$ $\underset{\left(0.057\right)}{-{0.144}^{**}}$ − − − Intercept −0.2 $\underset{\left(0.6194\right)}{-0.7331}$ $\underset{\left(0.6195\right)}{-0.7335}$ 2 $\underset{\left(0.4591\right)}{{2.6757}^{***}}$ $\underset{\left(0.4595\right)}{{2.6803}^{***}}$ ${\lambda }_{1}$ 0.4 $\underset{\left(0.0651\right)}{{0.2581}^{***}}$ $\underset{\left(0.0653\right)}{{0.2582}^{***}}$ 0.3 $\underset{\left(0.0463\right)}{{0.266}^{***}}$ $\underset{\left(0.0464\right)}{{0.267}^{***}}$ ${\lambda }_{2}$ −0.5 $\underset{\left(0.0753\right)}{-{0.5168}^{***}}$ $\underset{\left(0.0754\right)}{-{0.5171}^{***}}$ 0.5 $\underset{\left(0.0598\right)}{{0.7022}^{***}}$ $\underset{\left(0.0599\right)}{{0.703}^{***}}$ Covariance matrix structure DGP Estimated coef: Estimated coef: (4) (5) (6) ${\sigma }_{1}$ 2.1 $\underset{\left(0.1034\right)}{{2.4399}^{***}}$ $\underset{\left(0.1032\right)}{{2.4353}^{***}}$ ${\sigma }_{2}$ 3.1 $\underset{\left(0.1365\right)}{{2.7649}^{***}}$ $\underset{\left(0.1366\right)}{{2.763}^{***}}$ ${\rho }_{\eta }$ 0.7 $\underset{\left(0.0212\right)}{{0.7188}^{***}}$ $\underset{\left(0.0212\right)}{{0.7187}^{***}}$ ${\rho }_{\zeta }$ 0.5 $\underset{\left(0.0419\right)}{{0.529}^{***}}$ $\underset{\left(0.0419\right)}{{0.5301}^{***}}$ ${\rho }_{\epsilon }$ 0.4 $\underset{\left(0.1379\right)}{{0.6972}^{***}}$ $\underset{\left(0.1378\right)}{{0.697}^{***}}$