Identification analysis of DSGE models with DYNARE

by M. Ratto (Joint Research Centre)with contribution of N. Iskrev, Bank of Portugal

Discussion by Stephan Fahr, ECB(Usual disclaimer applies)

20 September 2011

DYNARE features

MODEL Simulation

Set parameters: parameter block Calibration: _steadystate.mUniqueness: steady (1 solution)Determinacy: checkSensitivity: dynare_sensitivity Moments, IRFs,

variance decomp.

Data

parametersMLEBayesian estimation (log-Likelihood)Shock decompositionGMM / SMM

Identification…

Identification…

Consistent story telling / policy implicationsAddressing specific questions: single parameter, modelling

block

Forecasting

Identification: what are the problems?

Objective: consistent story telling• How important is a specific parameter for the implications of

the model?

Moments (mean, variance, covariance, auto-covariance), impulse responses,…

• Potential problems:

1. Under-identification: parameter does not affect model moments.

2. Partial identification: only group of parameters affects model moments

Simulation delivers different results for different parameter values, but

data cannot pin down the specific parameter value.

3. Weak identification: parameters affects moments only little

Explanatory power of parameter is small / model is rigid

• Ultimately: how capable is the model (and its parameters) in replicating specific features of the data

• This is not about shock identification.

Features of the toolbox I

How well are parameters in DSGE models identified?• For assessment, Identification Toolbox exploits

• state equation

• first and second moments of the model.

• analytical derivatives

• efficient computation procedures.

• Issues covered

Non-identification based on rank deficiencies

1. Under-identification: Parameter does not affect moments

2. Partial identification: Parameters are collinear and cannot be identified seperably

3. Code identifies paramter(s) that lead to rank deficiency

Identification strength based on information matrix

1. T-test type analysis using parameter value and standard deviation

2. Weak identification through sensitivity of moments or near multi-collinearity

3. Normalisation of sensitivity measures (elasticities) to be unit-free.

Features of the toolbox II

Monte Carlo evaluation of parameter space

• Based on previous work on Global Sensitivity Analysis

• Drawing paramter combinations from prior parameter space

Discarded simulations (due to non-existant solution) reported individually.

Q: What are the parameter combinations?

Can common features of discarded simulations be reported?

Is the discarded parameter space covering a specific region?

How does sensitivity evolve once approaching the boundaries of the parameter space?

• Sensitivity measure based on cond. variance relative to uncond. variance

How much does output vary due to parameter? Procedure combines

1. Sensitivity of output vis-à-vis parameter and

2. Parameter uncertainty due to variance of prior distrbution

Usefulness as a tool

Identification toolbox addresses

• Main elements of local identification problems

• Easy and straightforward implementation (brief command)

• Helps to better understand the inner working of the model

• Many options require getting used to interpreting the output

Usefulness as a tool

Some issues / nice to haves

• Adding additional superfluous parameter led to error in my case. Possible bug?

• Example of perfect collinearityCollinearity patterns with 2 parameter(s)Parameter [ Expl. params ] cosne_a [ alp bet ] 1.000e_m [ bet rho ] 0.992alp [ e_a bet ] 1.000bet [ e_a alp ] 0.989gam [ mst del ] 0.701mst [ gam rho ] 0.701rho [ e_m del ] 0.992

• If collinearity is found, could one back out the equation?

• Illustration of IRF sensitivity for parameters with largest SVD would be interesting.

• Distinction if identification is based on 1st and/or 2nd moments. Relevant for 2nd moment / IRF matching

• How can higher-order moments help in better identifying parameters?

Next step (for the economist)

What to do if identification problems exist?

1. Find other data? YES: Concentrate on moments/ IRFs to be explained

NO: Identification problem is model issue, not data problem

2. Find model-external methods to identify parameters?YES, but gives rise to tensions between calibration and estimation

strategy

3. Change model blocks?YES: Toolbox gives indications on which parts to work