I’m currently writing a master thesis based on a modified version of Gertler and Karadi (G&K) “A model of unconventional monetary policy” (2011).
In line with G&K, I want to model government expenditures in a way, such that in steady state G/Y = g_ss = 0.2. However, I want government expenditures to be endogenous. I have seen an example in an article, where they write government expenditures as G_t = g_t*Y_t and let government expenditures evolve as: log(g_t) = (1-rho_g)*log(g_ss) + rgo_g*log(g_t-1) + sigma_g*epsilon_g.
I would like to take the same approach, but I’m not sure how to model it in Dynare. Currently I have:
exp(G)=exp(Y)*exp(g), and the shock as exp(g)=exp(g_ss)^(1-rho_g)*(exp(g(-1)))^rho_g*exp(epsi_g), where epsi_g is exogenous, and in my shocks block I have: var epsi_g; stderr sig_g; with sig_g=0.01, and in my initval block I have G=log(Y*g_ss). Is this the correct way to model it? My model is currently not running, but I’m not sure if the problem is due to the modelling of government expenditures or something else.
Furthermore, I’m quite unsure how to come up with good initial value guesses in the initval block. Currently I use the steady state values I know for sure, such as pi=1 etc, but how do one make good approximations for investment, capital, labor, wages, consumption etc.?