class: center, middle, inverse, title-slide # Participación laboral de las mujeres ## Macroeconomía Aplicada ### Maité y Marco Ramos ### 2020 --- # Adecuación del modelo canónico Problema del consumidor: `$$\sum_{t=0}^\infty \beta^t[U(C_t,L_t)]$$` `$$U(C_t,L_t)= \gamma log(C_t)+(1-\gamma)log(H-L_m-L_h)$$` `$$-$$` Adecuación: `$$\sum_{t=0}^\infty \beta^t[U(C_t,L_m^m,L^m_h,L_m^h,L_h^h)]$$` `$$U(C_t,L_t)= \gamma log(C_t)+\lambda(1-\gamma)log(H-L_m^m-L_h^m)$$` `$$+(1-\kappa)(1-\lambda)log(H-L_m^h-L_h^h)$$` `$$C_t=[\omega C_m^\eta+(1-\omega)C_h^\eta]^\frac{1}{\eta}$$` --- # Modelo neoclásico canónico `$$C_m+S=WL_m+RK$$` `$$K_{t+1}=(1-\delta)K_t+I_t$$` <br> Adecuación: `$$C_m+S=W_mL^m_m+WhL_m^h+RK$$` `$$K_{t+1}=(1-\delta)K_t+I_t$$` --- # Modelo neoclásico canónico Mercado de bienes `$$Y=AK^\alpha L_m^{1-\alpha}$$` `$$log A_t=(1-\rho_A)\overline{A}+\rho_AA_{t-1}+\epsilon_t^A$$` `$$max_{KL}=AK^\alpha L_m^{1-\alpha}-RK-WL_m$$` <br> Adecuación: `$$Y=AK^\alpha [\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{(1-\alpha)}{\xi}$$` `$$-$$` `$$max_{KL}=AK^\alpha [\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{(1-\alpha)}{\xi}-RK-W_mL^m_m-W_hL_m^h$$` --- # Modelo de producción doméstica caónico `$$C_h=BL_h^{\theta}$$` `$$log B_t=(1-\rho_B)\overline{B}+\rho_BB_{t-1}+\epsilon_t^B$$` Adecuación `$$C_h=B[\tau (L_h^m)^\psi + (1-\tau) (L_h^h)^\psi]^\frac{\theta}{\psi}$$` `$$-$$` --- # Condiciones de eficiencia (CPOS) `$$\frac{\gamma\omega C_m^{\eta-1}}{\omega C_m^\eta+(1-\omega)C_h^\eta}=\frac{\lambda(1-\gamma)}{W_m(H-L_m^m-L_h^m)}$$` `$$\frac{\gamma\omega C_m^{\eta-1}}{\omega C_m^\eta+(1-\omega)C_h^\eta}=\frac{(1-\lambda)(1-\gamma)}{2W_m(H-L_m^h-L_h^h)}$$` `$$\frac{\frac{ C_{m.t}^{\eta-1}}{\omega C_{m,t}^\eta+(1-\omega)C_{h,t}^\eta}}{\frac{ C_{m.t+1}^{\eta-1}}{\omega C_{m,t+1}^\eta+(1-\omega)C_{h,t+1}^\eta}}=\beta(1+R_{t+1)}-\delta)$$` --- # Condiciones de eficiencia (CPOS) `$$\frac{\gamma(1-\omega)C_h^{\eta-1}}{\omega C_m^\eta+(1-\omega)C_h^\eta}[\theta B[\tau (L_h^m)^\psi + (1-\tau) (L_h^h)^\psi]^\frac{\theta-\psi}{\psi}][\tau (L_h^m)^{\psi-1}]$$` `$$=\frac{\kappa(1-\gamma)}{(H-L_m^m-L_h^m)}$$` `$$\frac{\gamma(1-\omega)C_h^{\eta-1}}{\omega C_m^\eta+(1-\omega)C_h^\eta}[\theta B[\tau (L_h^m)^\psi + (1-\tau) (L_h^h)^\psi]^\frac{\theta-\psi}{\psi}][(1-\tau) (L_h^m)^{\psi-1}]$$` `$$=\frac{(1-\gamma) (1-\kappa)}{(H-L_m^h-L_h^h)}$$` --- # Condiciones de eficiencia (Vaciado) `$$Y_t=A_tK_{t-1}^\alpha [\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{(1-\alpha)}{\xi}$$` `$$C_h=B[\tau (L_h^m)^\psi + (1-\tau) (L_h^h)^\psi]^\frac{\theta}{\psi}$$` `$$K_t=T_t-C_{m,t}+K_{t-1}(1-\delta)$$` `$$I_t=Y_t-C_{m,t}$$` --- # Condiciones de eficiencia (Precios) `$$W_{m,t}=(1-\alpha)A_tK_{t-1}^\alpha[\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{1-\alpha-\xi}{\xi}[\nu (L_m^m)^{\xi-1}]$$` `$$W_{h,t}=(1-\alpha)A_tK_{t-1}^\alpha[\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{1-\alpha-\xi}{\xi}[(1-\nu) (L_m^h)^{\xi-1}]$$` `$$R_{t}=\alpha A_tK_{t-1}^{\alpha-1}[\nu (L_m^m)^\xi + (1-\nu) (L_m^h)^\xi]^\frac{1-\alpha}{\xi}$$` --- # Condiciones de eficiencia (Argumentos de perturbación) `$$log A_t=(1-\rho_A)\overline{A}+\rho_AA_{t-1}+\epsilon_t^A$$` `$$log B_t=(1-\rho_B)\overline{B}+\rho_BB_{t-1}+\epsilon_t^B$$` --- Bloque modelo canónico `\(\alpha\)` = 0.35; Garcia-Verdú (2005) `\(\beta\)` = 0.98; Rojas y Urrutia (2008) `\(\delta\)` = 0.05; Aguiar and Gopinath (2007) Bloque modelo de producción domestica `\(\gamma\)` = 0.83; calibración `\(\omega\)` = 0.417; McGrattan et al (1997) `\(\eta\)` = 0.80; Benhabid et al (1991) `\(\theta\)` = 0.85; flexibilización de Torres (2016) --- Bloque estocástico `\(\rho1\)` = 0.95; canónico/Torres (2016) `\(\rho2\)` = 0.95; canónico/Torres (2016) Bloque mercado laboral `\(\tau\)` = 0.52;calibración `\(\psi\)` = 0.70;calibración `\(\nu\)` = 0.40;calibración `\(\xi\)` = 0.35;calibración H = 1.00;normalización `\(\lambda\)` = .391;calibración --- Estado estacionario Y = 1.03976 I = 0.258433 K = 5.16866 R = 0.0704082 A = 1 B = 1 --- Estado estacionario `\(C_m\)` = 0.781326 `\(C_h\)` = 0.440972 `\(L_m^m\)` = 0.334074 `\(L_h^m\)` = 0.505643 `\(L_m^h\)` = 0.518598 `\(L_h^h\)` = 0.2599 `\(W_m\)` = 0.735758 `\(W_h\)` = 0.829247