linear form

[rama]

Hello everybody
I am trying to estimate a DSGE model with fiscal policy and I need someone to log-linearize these equations if it possible

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      tax_t    = τ_(c,t) c_t   +   τ_(l,t) w_t l_t  + τ_(k,t) r_t z_t k_t

    d_t= g_t  + (R_(t-1)/π_t )  d_(t-1)  -   tax_t 
 

thank you in advance

[ahnulxy]

You donot have to log-linearized the equations. Acutally, Dynare will help you do so if you put order=1 in stoch_simul command or estimation command.

[rama]

thank you for your reply but I inform you that the rest of my model is
log-linearized, so in my opinion I must linearize these equations to apply the command to estimate the overall model
what do you think ?
thank you

[jpfeifer]

Sorry to say this, but if your are not capable of loglinearizing your equations yourself, you should not be working with linearized models.

[rama]

thank you jpfeifer,
but the rest of my model is log linersed , so what I can execute my model with linear equations and nonlinear in the same time


tax_t = τ_(c,t) c_t + τ_(l,t) w_t l_t + τ_(k,t) r_t z_t k_t + τ_(k,t)(R_(t-1)-1) B_(t-1)/P_t

d_t= g_t + (R_(t-1)/π_t ) d_(t-1) - tax_t


tanks for your help

[jpfeifer]

This is possible, but rather involved. The nonlinear equations contain separate variables (e.g. y) that are not percentage deviations from steady state (e.g. yhat). To link them to the percentage deviations, you need to define them as separate variabes and link them to the linearized ones by

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y_hat=log(y)-log(steady_state(y))

For y you then need to provide steady state values.