Lectures in Monetary Economics - Harris Dellasharrisdellas.net/teaching/mon_econ/download/2010_szg_slides_7.pdf · Lectures in Monetary Economics Lecture 7 The DSGE model Lectures

Lectures in Monetary Economics Lecture 7 The DSGE model

Lectures in Monetary EconomicsLecture 7

The DSGE model

Harris Dellas

Department of EconomicsUniversity of Bern

December 9, 2009

Lectures in Monetary Economics Lecture 7 The DSGE modelThe DSGE model

The DSGE model

The baseline line version of the NK model seems to be a failure.Is it possible to improve its empirical performance?

Yes. But only by abandoning rationality and introducing arbitrary,controversial, non-rational features. In other words, by abandoningthe hard won discipline that Lucas and his followers brought to theprofession.


Figure: Inertia in the DSGE model


Two major modifications:

I In price setting

I In the formulation of real rigidities

A. Price setting: Baseline version

Optimizers:

Pot = (1− β(1− q))Et

∞∑τ=0

(1− q)τΛt+τ Ψt+τ (1)

Non-optimizers:Constant prices or prices indexed to steady state inflation.


B. Price setting: DSGE version

B1. Myopia in price setting

Optimizers, share 1− ω of population, Po

The same as in the baseline NK model

Non-optimizers (myopic), share ω of population, PN

PNt = Po

t−1 + πt−1

Pt = (1− q)Pt−1 + qPnewt

Pnewt = (1− ω)Po

t + ωPNt

This leads to a -hybrid- Phillips curve of the type

πt = γf Etπt+1 + γbπt−1 + λψt (2)

φ = (1− q) + ω(1− (1− q)(1− β))

λ = (1− ω)q(1− β(1− q))φ−1 (3)

γf = β(1− q)φ−1 (4)

γb = ωφ−1 (5)

(6)


B2. Backward indexation in price setting

An alternative (but quite similar) price setting scheme:

The non-optimizing firms set prices according to

Pit = ξtPit−1 (7)

ξt = πt−1 with πt = Pt/Pt−1. That is, the firms index their pricesto the lagged, economy wide rate of inflation.


Real rigidities

Preferences of the representative household

Et

∞∑τ=0

βτ

[log(ct+τ − ϑct+τ−1) +

νm

1− σm

(Mt+τ

Pt+τ

)1−σm

− νh

1 + σhh1+σh

t+τ

]

Habit persistenceBudget constraint

EtQtBt + Mt + Pt(ct + it + a(ut)kt) = Bt−1 + Mt−1 + Ptztutkt + Ptwtht + Ωt + Πt

Variable capital utilizationLaw of motion for capital

kt+1 = Φ(it , it−1, kt) + (1− δ)kt

Either capital or investment adjustment costs


Evaluation: Empirical success. The model manages to generateinertia (Christiano et al., 2005). But still too much nominalrigidity. Altig et al. 2005 try to fix it but run into other problems.


What are the critical elements?Examine the properties of the model under

I An exogenous money supply rule

I A Taylor rule

2. Various forms of nominal rigidities.

I Only prices are sticky and wages are flexible, q = 0.25 (pricecontracts of 4 quarters).

I Both prices and wages are sticky. Following Christiano et al.we set qp = 0.50 and qw = 0.30: prices are reset on averageevery semester, while it takes 3 quarters on average to resetwages.


With real rigidities but no price indexation

I The model fails to generate inflation inertia independent ofthe type(s) of real rigidity considered.

I Output inertia does not obtain under any single real rigiditybut emerges when all of them are combined together.

I Investment adjustment costs are the only feature that canhelp the model produce a liquidity effect.

I Problems with unconditional moments (investment is notvolatile enough and inflation is too volatile.

I It implies strong countercyclicality in the real and nominalinterest rate.

I An informational lag: Observing the growth rate of the moneysupply with a one period lag does not help.


Introduce price indexation on top of the real rigidities

I First, the model can now generate inflation persistence.

I Lagged indexation is not sufficient for that, the model alsoneeds to include investment adjustment costs.

I The same real rigidity is also responsible for a liquidity effect.

I The other real rigidities do not contribute to inflation inertiabut all together they help generate inertial output dynamics.

I Predetermined expenditure is particularly important for thelast pattern.

I But he model does not perform noticeably better relative tothe standard version with regard to unconditional moments.The same weaknesses are observed, in particular with regardto the cyclical properties of the interest rates.


From these findings one can claim that the existence of the priceindexation scheme is sina qua non for the ability of the Keynesianmodel to produce inflation inertia.

Nominal wage rigidities are claimed by Christiano et al, 2005, to bethe dominant source of nominal rigidity.

We repeat the preceding analysis using nominal wage in place ofprice rigidity.

The dynamic patterns are virtually identical to those obtainedunder price rigidity.


I No inflation inertia ever obtains no matter what type(s) ofreal rigidities are present.

I When all the real rigidities are combined together then themodel produces hump shaped dynamics for output and aliquidity effect (due mostly to investment adjustment costs).

I The overall performance of the model as judged by theunconditional moments is worse relative to the case of pricerigidities because of excessively large volatility.

I The strong countercyclicality in interest rates remains.


The role of the price re-setting scheme (Calvo vs Taylor)Random Duration (Calvo)Non-optimizing firms


ξt = πt−1 or ξt = π.

Optimizing firms: The usual

The aggregate price level is

Pt =(qP?t

1−θ + (1− q)(ξtPt−1)1−θ) 1

1−θ

(9)


Fixed DurationIntermediate producers set prices for N periods of time in astaggered fashion.In each and every period, a fraction 1/N of producers chooses anew optimal price P?

t (i). During the following N − 1 periods thisprice evolves according to


with either ξt = π or ξt = πt−1 as in the Calvo case above.Prices are set so as to maximize the expected sum of discountedprofits from period t to period t + N − 1.The aggregate price index is

Pt =

(1

N

N−1∑τ=0

(Ξt−τ,τP?t−τ )1−θ

) 11−θ

(11)


Main findings:With the help of backward indexation the model can generateinflation inertia independent of the price setting mechanism (Calvovs Taylor).

But it needs more price stickiness under the Taylor scheme in orderto generate sufficient inertia in output.


Figure: The role of the price resetting scheme: Fixed (Taylor) vs Random(Calvo) (a) 2 periods

0 5 10 15−0.5

0

0.5

1Output

FixedRandom

0 5 10 15−0.5

0

0.5

1

1.5Inflation

(b) 4 periods

0 5 10 15−0.5

0

0.5

1

1.5

2Output

FixedRandom

0 5 10 15−0.2

0

0.2

0.4

0.6

0.8Inflation

(c) 6 periods

0 5 10 15−1

0

1

2

3Output

FixedRandom

0 5 10 15−0.2

0

0.2

0.4

0.6Inflation

(d) 8 periods

0 5 10 15−1

0

1

2

3

4Output

FixedRandom

0 5 10 15−0.2

0

0.2

0.4

0.6Inflation


Overall Evaluation

Overall EvaluationThe DSGE model seems to work well empirically. But this requiresnon-rational price setting schemes and also ”novel” real rigidities.A. What is the problem with the backward indexation assumption?

I Conceptually: It violates strict rationality. Feasible, alternativeindexation schemes lead to higher profits (for indexation toexpected rather than past inflation or to R) and eliminateinertia.

I It is at variance with the empirical evidence regarding pricingbehavior (Dhyne et al. 2005). Individual price changes do notmove in tandem with aggregate inflation. Unlike the laggedindexation assumption which implies that all individual pricesmove roughly at the rate of aggregate inflation ”. . . individualprice changes are sizeable compared to the inflation rateprevailing in each country . . . ”(Dhyne et al. 2005).

Note that the arguments of Eichenbaum and Fisher, 2004 and DeWalque, Smets and Wouters, 2005, cannot save the model.B. Moreover, other empirical problems remain (credibility, Eulereqs ...)


Overall Evaluation

Model Structure:

AgentsThere are five different types of economic agents:

I households: consume, invest in physical capital, supplydifferentiated labor services, set wages, trade in domestic andforeign bonds.

I intermediate-good firms: use labor and capital as inputs,produce differentiated goods sold domestically and abroad, setprices.

I final-good firms: combine domestic and foreign intermediategoods to produce final goods used for domestic private andpublic consumption and investment purposes.

I the fiscal authority: purchases public consumption goods,issues bonds, levies distortionary and lump-sum taxes.

I the monetary authority: sets the nominal interest rate byfollowing a Taylor-type interest-rate rule.

International linkages arise from trade in intermediate goods(accounting for imperfect exchange-rate pass-through) and foreignbonds.


Overall Evaluation

FrictionsHouseholds and firms face various frictions which makeadjustments costly (useful for generating inertia).

I external habit formation in consumption

I generalized adjustment cost in investment

I fixed cost in intermediate-good production

I monopolistic competition in intermediate-good and labormarkets

I sticky prices and wages a la Calvo and (partial) backwardindexation

I adjustment cost in imports

I financial frictions in form of an ”external finance premium”and intermediation costs for trading foreign bonds.


Overall Evaluation

The estimated version of the model uses 17 macroeconomic timeseries to estimate parameters.A corresponding number of 17 structural shocks have been includedto capture the stochastic nature of the macroeconomic data.Besides checking formal statistical criteria, the estimated model isvalidated by assessing:

I the propagation of structural shocks through the economy(IRFs)

I the contribution of structural shocks to economic fluctuations(forecast error- variance decompositions)

I the implied variability and persistence of observed variables(standard deviations and autocorrelation functions)

I the out-of-sample forecasting performance (rootmean-squared errors)

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Lectures in Monetary Economics - Harris Dellasharrisdellas.net/teaching/mon_econ/download/2010_szg_slides_7.pdf · Lectures in Monetary Economics Lecture 7 The DSGE model Lectures