3. DSGE-VAR Modeling

3.1. Description

The DSGE-VAR or elswhere known as BVAR-DSGE is a methodology that combines a BVAR and a DSGE model following the methodology in [Del Negro and Schorfheide, 2004] and [Del Negro et al., 2007].

There are two possible interpretations. One is that the DSGE is used as a prior for the BVAR model and the other is that the BVAR serves to relax the tight restrictions in the DSGE model.

In the end we have four sub-models in one object:

The VAR model

The VAR approximation of the DSGE model

The DSGE model

The BVAR model i.e. the VAR model with the (VAR approximation of the) DSGE as prior

In RISE, the DSGE model can be a model with a simple instrument rule (e.g. Taylor rule) or an optimal policy under commitment or under discretion.

The DSGE model can be stationary or nonstationary.

3.2. A quick-start example

3.2.1. A simple New Keynesian DSGE model

dsgemodel={
'model:New Keynesian model'
'@endogenous X "Output gap" R "interest rate" P "Inflation" G U'
'@exogenous EG "Demand shock" EU "Monetary Policy shock"'
'@parameters beta "discount factor" kappa "Phillips curve slope" sigu sigg rhou rhog psi'
'@observables  P R'
'@model'
'       P = beta*P{+1}+kappa*X;'
'       X = X{+1}-(R-P{+1}-G);'
'       R = psi*P+U;'
'       U = rhou*U{-1} + sigu*EU;'
'       G = rhog*G{-1} + sigg*EG;'
    };

3.2.2. Setting up the BVAR-DSGE model

nlags=4;

constant=false;

mdl=bvar_dsge(dsgemodel,nlags,constant);

3.2.3. Fixed parameters

mdl=set(mdl,'parameters',{'beta',0.96});

3.2.4. Setting up and visualing the priors

priors=struct();

% ___priors on the DSGE parameters___
priors.kappa={0.2,0.5,0.5,'gamma'};
priors.psi={1.5,2,.5,'gamma'};
priors.rhou={0.75,0.75,0.1,'beta'};
priors.rhog={0.75,0.75,0.1,'beta'};
priors.sigu={0.01,0.01,4,'sichisq'};
priors.sigg={0.01,0.01,4,'sichisq'};

% ___prior on the dsge model___
priors.dsge_prior_weight={3,3,1,'gamma'};

plotOpts=struct();
plotOpts.prior_trunc=2e-3;
rdist.plot(priors,plotOpts)

3.2.5. Collecting and transforming the data

d=fetch_fred({'CPALTT01USQ661S','BOGZ1FL072052006Q'});

db=struct();

db.P=log(d(1).series/lag(d(1).series,1));

db.R=d(2).series/100;

3.2.6. Maximizing the posterior

mdlest=estimate(mdl,'priors',priors,'data_demean',true,'data',db,...
    'estim_start_date','1960Q2','estim_end_date','2022Q3');

3.2.7. IRFs of the BVAR-DSGE at the maximized posterior

myirfs_bvar_dsge=irf(mdlest);

3.2.8. IRFs of the DSGE model at the maximized posterior

myirfs_dsge=irf(mdlest.dsge);

3.2.9. IRF comparison

myirfs=ts.concatenator(myirfs_bvar_dsge,myirfs_dsge)

quick_irfs(mdlest.dsge,myirfs,{'P','R'})

3.3. Technical documentation for dsge_var objects