inflation in DSGE

[ecrgap]

Dear Tom

Is there available a code for the calibration of a simple DSGE New Keynesian model for output inflation and the interest rate?
In the forum I can find only codes for RBC models. I need that because I want to see how we introduce the inflation rate into the code.

Thank you very much in advance

Best

[TomDoan]

This is the EHL model. Did you have a different one in mind?

Code: Select all

*
* Model from Erceg, Henderson & Levin(2000), "Optimal monetary policy
* with staggered wage and price contracts," Journal of Monetary
* Economics, vol. 46, no 2, 281-313.
*
dec series g mpl mrs dp dw realw r y
dec series rstar wstar ystar
dec series x u z
*
dec real beta sigma chi alpha thetaW thetaP xiW xiP
dec real ubar zbar xbar kbar
dec real rhox
dec real lbar ybar cbar
dec real kappaP kappaW
*
* Household parameters
*
compute beta      = .99
compute sigma     = 1.5
compute chi       = 1.5
compute ubar      = 0.3163
compute zbar      = 0.03
*
* Production function parameters
*
compute alpha     = .3
compute rhox       = 0.95
compute xbar      = 4.0266
compute kbar      = 30.0*ubar
*
* Calvo process parameters
*
compute thetaW    = 1.0/3.0
compute thetaP    = 1.0/3.0
compute xiW       = .75
compute xiP       = .75

compute eps       = 6.0
compute phi       = 6.0
*
* Policy parameters
*
compute rhor       = 0.9
compute gammapi    = 2.0
compute gammaogap = 0.125
*
compute lbar      = .27
compute ybar      = 10.0*ubar
compute cbar      = ybar
*
* Simplifications depending upon deep parameters
*
compute lcbar     = cbar/(cbar-ubar)
compute lubar     = ubar/(cbar-ubar)
compute llbar     = lbar/(1-lbar-zbar)
compute lzbar     = zbar/(1-lbar-zbar)
compute lambda    = alpha + chi * llbar + (1-alpha) * sigma * lcbar
compute kappaP    = (1-xiP*beta)*(1-xiP)/xiP
compute kappaW    = (1-xiW*beta)*(1-xiW)/(xiW*(1+chi*llbar*((1+thetaW)/thetaW)))
*
frml(identity) eqn1  = g     - (g{-1} - 1.0/(sigma*lcbar)*(r{0}-dp{-1}-rstar{0}))
frml(identity) eqn2  = mpl   - (wstar{0} - alpha/(1+alpha)*g{0})
frml(identity) eqn3  = mrs   - (wstar{0} + (chi*llbar/(1-alpha) + sigma*lcbar)*g{0})
frml(identity) eqn4  = dp    - (beta*dp{-1}+kappaP*(realw-mpl))
frml(identity) eqn5  = dw    - (beta*dw{-1}+kappaW*(mrs-realw))
*
* Pareto optima
*
frml(identity) opt1 = ystar - (((1-alpha)*sigma*lubar/lambda)*u{0}-(1-alpha)*chi*lzbar/lambda*z{0}+(1+chi*llbar)/lambda*x{0})
frml(identity) opt2 = wstar - ((-alpha*sigma*lubar/lambda)*u{0}+alpha*chi*llbar/lambda*z{0}+(chi*llbar+alpha*lcbar)/lambda*x{0})
frml(identity) opt3 = rstar - (sigma*lcbar*(ystar{-1}-ystar)+sigma*lubar*(u{-1}-u))
*
frml(identity) def1  = realw - (realw{1}+dw-dp)
frml(identity) def2  = g     - (y - ystar)
*
* The model above needs to be closed with a rule for setting the interest rate
*
frml(identity) c1   = r     - (rhor*r{1}+(1-rhor)*(gammapi*dp+gammaogap*g))
*
frml           s1    = (x-xbar)-(rhox*(x{1}-xbar))
frml           s2    = (u-ubar)
frml           s3    = (z-zbar)

group dsge eqn1 eqn2 eqn3 eqn4 eqn5 opt1 opt2 opt3 def1 def2 s1 s2 s3 c1
dsge(model=dsge,a=adlm,f=fdlm) g dp dw y mpl mrs realw ystar wstar rstar x u z r
@dlmirf(page=byshock,a=adlm,f=fdlm,$
  shocks=||"Productivity","Consumption","Leisure"||,$
  variables=||"Gap","Price Inflation","Wage Inflation"||)

[ecrgap]

That is exactly what I had in mind.

I really appreciate

[jdacuddy]

Dear Tom,

You asked about other DSGE models. One which is rather prominent is:

Lubik, Thomas A. & Schorfheide, Frank, 2007. "Do central banks respond to exchange rate movements? A structural investigation," Journal of Monetary Economics, vol. 54(4), pages 1069-1087, May 2007

Code exists for this under Dynare (see "http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=1689&p=4228&hilit=lubik#p2925"), but it would be very interesting to compare results and functionality with RATS if you had RATS code for it.

Regards

[TomDoan]

You can see how this looks.

Code: Select all

*
* Model from Lubik, Thomas A. & Schorfheide, Frank, 2007. "Do central
* banks respond to exchange rate movements? A structural investigation,"
* Journal of Monetary Economics, vol. 54(4), pages 1069-1087, May 2007
*
dec series y phi r q exch A phistar ystar
dec series er eq eystar ephistar ez
dec real beta tau k alpha rhor rhoq rhoystar rhophistar rhoz gamma1 gamma2 gamma3
*
compute beta=0.96
compute tau=0.5
compute k=0.5
compute alpha=0.10
compute rhor=0.5
compute rhoq=0.4
compute rhoystar=0.9
compute rhophistar=0.8
compute rhoz=0.2
compute gamma1=1.5
compute gamma2=0.25
compute gamma3=0.25
frml(identity) eqn1 = y - (y{-1}-(tau+alpha*(2-alpha)*(1-tau))*(r-phi{-1})-rhoz*(A-A{1})-$
   alpha*(tau+alpha*(2-alpha)*(1-tau))*q{-1}+alpha*(2-alpha)*((1-tau)/tau)*(ystar))
frml(identity) eqn2 = phi - (beta*phi{-1}+alpha*beta*q{-1}-(alpha*q)+(k/(tau+alpha*(2-alpha)*(1-tau)))*$
     (y+alpha*(2-alpha)*((1-tau)/tau)*ystar))
frml(identity) eqn3 = r - (rhor*r{1}+(1-rhor)*(gamma1*phi+gamma2*y+gamma3*exch)+er)
frml(identity) eqn4 = exch - (phi-(1-alpha)*q-phistar)
frml(identity) eqn5 = q - (rhoq*q{1}+eq)
frml(identity) eqn6 = A - (A{1}+ez)
frml(identity) eqn7 = phistar - (rhophistar*phistar{1}+ephistar)
frml(identity) eqn8 = ystar - (rhoystar*ystar{1}+eystar)
frml           eqn9 = er
frml           eqn10 = eq
frml           eqn11 = eystar
frml           eqn12 = ephistar
frml           eqn13 = ez
group dsge eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqn8 eqn9 eqn10 eqn11 eqn12 eqn13
dsge(model=dsge,a=adlm,f=fdlm,z=zdlm) y phi r q exch A phistar ystar er eq eystar ephistar ez
@dlmirf(a=adlm,f=fdlm,page=byshock,$
  shocks=||"R","Q","YSTAR","PHISTAR","Z"||,$
  variables=||"Y","PHI","R","Q","EXCH","A"||)

[jdacuddy]

Thank you, Tom, for your amazingly quick reply. I will look into it immediately.
Regards

[jdacuddy]

Dear Tom,

Following up on this, having run it, I conclude that the code you posted seems to provide almost exactly the same IRFs as does the Dynare code for the calibrated model; thank you! A natural next step would be to estimate (some of) the parameters, rather than calibrate everything. This is easily done in Dynare; is it possible in RATS? If so, the next step would be to use the estimated DSGE to provide a prior for a BVAR. Again, this is easily done in Dynare; could you explain how (if at all) it can be done in RATS?

Regards

[ecrgap]

Thank you all for your great help

[TomDoan]

Dear Tom,

Following up on this, having run it, I conclude that the code you posted seems to provide almost exactly the same IRFs as does the Dynare code for the calibrated model; thank you! A natural next step would be to estimate (some of) the parameters, rather than calibrate everything. This is easily done in Dynare; is it possible in RATS? If so, the next step would be to use the estimated DSGE to provide a prior for a BVAR. Again, this is easily done in Dynare; could you explain how (if at all) it can be done in RATS?

Regards

An example of estimation is provided in http://www.estima.com/forum/viewtopic.php?f=26&t=310.

The attached procedure

varfromdlm.src

(2.58 KiB) Downloaded 237 times

converts a selection of variables out of a state space model to their representation as a VAR.

[jdacuddy]

Thank you, Tom. I should have thought of the Ireland example myself!
Regards

[ecrgap]

Hi all,

I want to calibrate a DSGE model where the Central Bank uses a threshold interest rate rule (say of TAR form). I guess the model must be simulated in order to generate the IRFs. Is there any sample any model that has done something like that?

Thanks

[ivory4]

Lubik and Shorfheide (2004 AER) Testing for Indeterminacy:An Application to U.S. Monetary Policy

Is there code for this paper? Or some suggestions on this one?