Hi Prof. Pfeifer,

May I ask which utility function you used in your BCA replication of Chari et. al paper. From euler equation in the mod file,

(1+{{\tau_x}_{t}}) ({{c}_{t}})^{(-{{\sigma}})} (1-({{l}_{t}}))^{{{\psi}} (1-{{\sigma}})}={{\hat \beta}} ({{c}_{t+1}})^{(-{{\sigma}})} (1-({{l}_{t+1}}))^{{{\psi}} (1-{{\sigma}})} ((1-{{\delta}}) (1+{{\tau_x}_{t+1}})+(({{l}_{t+1}}) ({{z}_{t+1}}))^{1-{{\theta}}} {{\theta}} ({{k}_{t}})^{{{\theta}}-1})

it seems U = \frac{{{c}_{t}}^{(1-{{\sigma}})} }{1-{{\sigma}}} (1-({{l}_{t}}))^{{{\psi}}\, (1-{{\sigma}})}.

But that suggests the following intratemporal condition: \frac{{{\psi}}\, \left({{c}_{t}}\right)^{{{}}}}{1-\left({{l}_{t}}\right)}=\left(1-{{\tau_l}_{t}}\right)\, \left({{w}_{t}}\right) . And not \frac{{{\psi}}\, \left({{c}_{t}}\right)^{{{\sigma}}}}{1-\left({{l}_{t}}\right)}=\left(1-{{\tau_l}_{t}}\right)\, \left({{w}_{t}}\right) used in the mod file. It does not affect the results though. But is this the utility function you used for the replication?

Also, you use the following law of motion for capital;

\left(1+\gamma_{z}\right)\left(1+\gamma_{n}\right)\left(k_{t}\right)=\left(x_{t}\right)+(1-\delta)\left(k_{t-1}\right), suggesting k_t = \frac{K_t}{N_t Z_t}

And the paper uses;

\left(1+\gamma_{n}\right)\left(k_{t}\right)=\left(x_{t}\right)+(1-\delta)\left(k_{t-1}\right), suggesting k_t = \frac{K_t}{N_t}, I guess.

Is it just a matter of preference which one to use?