on the welfare costs of monetary policy

On the Welfare Costs of Monetary Policy

Jean Blaise Nlemfu M.

Department of EconomicsUniversity of Quebec at Montreal

June 2016

Jean Blaise Nlemfu M. ( Department of Economics University of Quebec at Montreal) June 2016 1 / 25

Outline1 Introduction

BackgroundWhat This Paper DoesFindingsRelated literature

2 ModelFirms and Price settingHouseholds and Wage settingMonetary PolicyAggregationWelfare

3 Calibration4 Results

Welfare costsVolatilitiesImpulse Responses Analysis

5 ConclusionJean Blaise Nlemfu M. ( Department of Economics University of Quebec at Montreal) June 2016 2 / 25

Background

Clarida, Gali, and Gertler (2000) explore the role of monetary policy.

They estimate a taylor type monetary policy rulecombine it with a calibrated sticky-price model with zero trend inflationLubik and Schorfheide(2004);Zandweghe, Hirose and Kurozumi (2015).

Coibion and Gorodnichenko (2011)

Based on an estimated Taylor rulecalibrated staggered-price model with non-zero trend inflationAscari, Branzoli and Castelnuovo (2015)

However, the aforementioned literature has been silent about thewelfare implications.


Background

Clarida, Gali, and Gertler (2000) explore the role of monetary policy.They estimate a taylor type monetary policy rule

combine it with a calibrated sticky-price model with zero trend inflationLubik and Schorfheide(2004);Zandweghe, Hirose and Kurozumi (2015).





Background

Clarida, Gali, and Gertler (2000) explore the role of monetary policy.They estimate a taylor type monetary policy rulecombine it with a calibrated sticky-price model with zero trend inflation

Lubik and Schorfheide(2004);Zandweghe, Hirose and Kurozumi (2015).Coibion and Gorodnichenko (2011)




Background

Clarida, Gali, and Gertler (2000) explore the role of monetary policy.They estimate a taylor type monetary policy rulecombine it with a calibrated sticky-price model with zero trend inflationLubik and Schorfheide(2004);Zandweghe, Hirose and Kurozumi (2015).





Background


Coibion and Gorodnichenko (2011)Based on an estimated Taylor rule

calibrated staggered-price model with non-zero trend inflationAscari, Branzoli and Castelnuovo (2015)



Background


Coibion and Gorodnichenko (2011)Based on an estimated Taylor rulecalibrated staggered-price model with non-zero trend inflation

Ascari, Branzoli and Castelnuovo (2015)However, the aforementioned literature has been silent about thewelfare implications.


Background


Coibion and Gorodnichenko (2011)Based on an estimated Taylor rulecalibrated staggered-price model with non-zero trend inflationAscari, Branzoli and Castelnuovo (2015)



What This Paper Does

Analyzes the implications of policy changes for the welfare.

Using a medium-scale DSGE modelInspired by Ascari, Phaneuf and Sims (2015)An extended work along with :

A split sample : 1960:I -1983:IV and 1984:I - 2007:III.A calibrated Fed’s reaction function based on estimates in the literatureand combine it with our calibrated medium-scale New Keynesian model.structural parameters do not change except for shocks parametersTrend inflation and real per capita output growth are set at theirobserved values in each sample period.

Explores the link between shifting non-zero trend inflation andmacroeconomic variables volatilities.



Analyzes the implications of policy changes for the welfare.Using a medium-scale DSGE model

Inspired by Ascari, Phaneuf and Sims (2015)An extended work along with :





Analyzes the implications of policy changes for the welfare.Using a medium-scale DSGE modelInspired by Ascari, Phaneuf and Sims (2015)

An extended work along with :





Analyzes the implications of policy changes for the welfare.Using a medium-scale DSGE modelInspired by Ascari, Phaneuf and Sims (2015)An extended work along with :






A split sample : 1960:I -1983:IV and 1984:I - 2007:III.

A calibrated Fed’s reaction function based on estimates in the literatureand combine it with our calibrated medium-scale New Keynesian model.structural parameters do not change except for shocks parametersTrend inflation and real per capita output growth are set at theirobserved values in each sample period.





A split sample : 1960:I -1983:IV and 1984:I - 2007:III.A calibrated Fed’s reaction function based on estimates in the literature

and combine it with our calibrated medium-scale New Keynesian model.structural parameters do not change except for shocks parametersTrend inflation and real per capita output growth are set at theirobserved values in each sample period.





A split sample : 1960:I -1983:IV and 1984:I - 2007:III.A calibrated Fed’s reaction function based on estimates in the literatureand combine it with our calibrated medium-scale New Keynesian model.

structural parameters do not change except for shocks parametersTrend inflation and real per capita output growth are set at theirobserved values in each sample period.





A split sample : 1960:I -1983:IV and 1984:I - 2007:III.A calibrated Fed’s reaction function based on estimates in the literatureand combine it with our calibrated medium-scale New Keynesian model.structural parameters do not change except for shocks parameters

Trend inflation and real per capita output growth are set at theirobserved values in each sample period.



Findings

Welfare costs respond symmetrically to a rise and a decline in trendinflation, trend growth and the level of volatility over the pre- andpost-1984 periods.

An increase in the variance of shocks to the trend inflation processincreases means welfare costs by increasing the volatilities of outputand inflation in the pre-1984 period (Christiano, 2015).welfare costs in the post-1984 period are modest.

Changes in the Fed’s response to macroeconomic variables along withthe decline in trend inflation are the main sources of the shift inmacroeconomic variables volatilities (Coibion and Gorodnichenko,2011 and Arias, Ascari, Branzoli and Castelnuovo, 2015).


Findings


An increase in the variance of shocks to the trend inflation processincreases means welfare costs by increasing the volatilities of outputand inflation in the pre-1984 period (Christiano, 2015).

welfare costs in the post-1984 period are modest.Changes in the Fed’s response to macroeconomic variables along withthe decline in trend inflation are the main sources of the shift inmacroeconomic variables volatilities (Coibion and Gorodnichenko,2011 and Arias, Ascari, Branzoli and Castelnuovo, 2015).


Findings


An increase in the variance of shocks to the trend inflation processincreases means welfare costs by increasing the volatilities of outputand inflation in the pre-1984 period (Christiano, 2015).welfare costs in the post-1984 period are modest.

Changes in the Fed’s response to macroeconomic variables along withthe decline in trend inflation are the main sources of the shift inmacroeconomic variables volatilities (Coibion and Gorodnichenko,2011 and Arias, Ascari, Branzoli and Castelnuovo, 2015).


Related literature

This paper is in line with a set of papers that examines the effects ofnon-zero trend inflation:

Ascari and Ropele (2007)Amano, Moran, Murchison, and Rennison (2009)Amano, Ambler, and Rebei (2007)Kiley (2007), Ascari and Ropele (2009), and Coibion andGorodnichenko (2011)This paper differs from the aforementioned :

it studies the implications of monetary policy changes for the welfarecosts over the pre- and post-1984.

The paper closest to ours : Ascari, Phaneuf and Sims (2015).Our paper is also closely related to Clarida, Gali, and Gertler (2000).


Related literature


Ascari and Ropele (2007)

Amano, Moran, Murchison, and Rennison (2009)Amano, Ambler, and Rebei (2007)Kiley (2007), Ascari and Ropele (2009), and Coibion andGorodnichenko (2011)This paper differs from the aforementioned :




Related literature


Ascari and Ropele (2007)Amano, Moran, Murchison, and Rennison (2009)

Amano, Ambler, and Rebei (2007)Kiley (2007), Ascari and Ropele (2009), and Coibion andGorodnichenko (2011)This paper differs from the aforementioned :




Related literature


Ascari and Ropele (2007)Amano, Moran, Murchison, and Rennison (2009)Amano, Ambler, and Rebei (2007)

Kiley (2007), Ascari and Ropele (2009), and Coibion andGorodnichenko (2011)This paper differs from the aforementioned :




Related literature


Ascari and Ropele (2007)Amano, Moran, Murchison, and Rennison (2009)Amano, Ambler, and Rebei (2007)Kiley (2007), Ascari and Ropele (2009), and Coibion andGorodnichenko (2011)

This paper differs from the aforementioned :




Related literature






Related literature




The paper closest to ours : Ascari, Phaneuf and Sims (2015).

Our paper is also closely related to Clarida, Gali, and Gertler (2000).


Related literature






Final Goods Producers

Composite gross output :

Xt =(∫ 1

0Xt(j)

θ−1θ dj

) θθ−1

(1)

Input-demand function for the intermediate good :

Xt(j) =(Pt(j)

Pt

)−θXt , ∀j, (2)

Aggregate price indexe :

P1−θt =

∫ 1

0Pt(j)1−θdj (3)


Intermediate Producers

The production function for a typical intermediate producer j :

Xt(j) = max{

AtΓt(j)φ(Kt(j)αLt(j)1−α

)1−φ−ΥtF , 0

}, (4)

F is a fixed cost, and production is required to be non-negative.Υt is a growth factor and F is chosen to keep profits zero along abalanced growth path.At follows a process with both a trending and stationary component :

At = AtAτt , (5)

Aτt = gAAτ

t−1 (6)

The stochastic process driving the detrended level of technology At isgiven by

At =(At−1

)ρA exp(sAuA

t

), 0 ≤ ρA< 1 (7)


Profit Maximization and Price Setting

Firms set their price according to Calvo pricingSince all updating firms will choose the same reset price, the optimalreset price relative to the aggregate price index is p∗t ≡

P∗t

Pt.

The optimal pricing condition can be written:

p∗t = θ

θ − 1x1,tx2,t

. (8)

The auxiliary variables x1,t and x2,t can be written recursively :

x1,t = λrt νtXt + βξpEt(πt+1)θx1,t+1, (9)

x2,t = λrt Xt + βξpEt(πt+1)θ−1x1,t+1. (10)


Labor Composite

The composite labor input is :

Lt =(∫ 1

0Lt(i)

σ−1σ di

) σσ−1

(11)

The input demand for labor of type-i :

Lt(i) =(Wt(i)

Wt

)−σLt (12)

The aggregate wage indexe is :

W 1−σt =

∫ 1

0Wt(i)1−σdi (13)


Utility Maximization

The problem of a typical household :

maxCt ,Lt(i),Kt+1,Bt+1,It ,Zt

E0

∞∑t=0

βt(

ln (Ct − bCt−1)− ηLt(i)1+χ

1 + χ

)

subject to

Pt

(Ct + It + a(Zt)Kt

εI ,τt

)+ Bt+1

1 + it≤ Wt(i)Lt(i) + Rk

t ZtKt + Πt + Bt + Tt

wherea(Zt) = γ1(Zt − 1) + γ2

2 (Zt − 1)2


Utility Maximization

and the physical capital accumulation process,

Kt+1 = εI ,τt ϑt

(1− S

( ItIt−1

))It + (1− δ)Kt . (14)

Investment adjustment cost

S( It

It−1

)= κ

2

( ItIt−1

− 1)2, (15)

Two types of investment shocks (Justiniano et al., 2011)IST, shocks map one-to-one into the relative price of investmentgoodsMEI, ϑt , shocks do not impact the relative price of investmentwith

ϑt = (ϑt−1)ρI exp(sI uI

t

), 0 ≤ ρI < 1. (16)


Wage setting

Households update their wages each period with the probability(1− ξw).The first order condition gives the following optimal wage :

w∗t = σ

σ − 1f1,tf2,t

. (17)

Recursively the terms f1,t and f2,t give the following :

f1,t = η

(wtw∗t

)σ(1+χ)L1+χ

t + βξwEt(πt+1)σ(1+χ)(w∗t+1

w∗t

)σ(1+χ)f1,t+1,

(18)and

f2,t = λrt

(wtw∗t

)σLt + βξwEt(πt+1)σ−1

(w∗t+1w∗t

)σf2,t+1. (19)


Monetary Policy

Monetary policy consists of a talor-type rule

1 + it1 + i =

(1 + it−11 + i

)ρi [(πtπ

)απ( Yt

Yt−1g−1

Y

)αy]1−ρi

εrt . (20)

with it and i the nominal and steady state interest rate respectevelyπtπ the inflation gap,Yt

Y the output gap and ρi the interest ratesmootingαπ and αy the control parametersεr

t an exogenous shock to the policy rule, εrt∼iid

(0, σ2

εr).


Aggregation

The aggregate input demands :

Γt(j) = φmct (stXt(j) + ΥtF) , (21)

Kt(j) = α(1− φ)mctrk

t(stXt(j) + ΥtF) , (22)

Lt(j) = (1− α)(1− φ)mctwt

(stXt(j) + ΥtF) . (23)

The Real GDP or Aggregate net output, Yt is given by :

Yt = Xt − Γt (24)

The aggregate resource constraint is given by

Yt = Ct + It + a(Zt)εI ,τ

tKt (25)


Welfare

Aggregate Welfare :

Wt = ln(Ct − bCt−1)− ηvwt

L1+χt

1 + χ+ βEtWt+1 (26)

where vwt is the wage dispersion and is given by :

vwt = (1− ξw)

(w∗twt

)σ(1+χ)+ ξw

(wtπtwt−1

)σ(1+χ)vw

t−1 (27)


Calibration

Baseline calibration

Non-shock parameters

Non-shock parameters, pre-1984 (see Table 1 )Non-shock parameters, post-1984 (see Table 2 )

Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration

Baseline calibrationNon-shock parameters




Calibration


Non-shock parameters, pre-1984 (see Table 1 )

Non-shock parameters, post-1984 (see Table 2 )Shock parameters (see Table 3 )

Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration





Calibration



Shock parameters (see Table 3 )

Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )

We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)

Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.

The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the data

The trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capita

Trend inflation is set at its observed value in each period.Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration



Shock parameters (see Table 3 )Alternative calibration (see Table 4 )We use series from the Bureau of Economic Analysis (BEA)Based on a split sample : 1960:I -1983:IV and 1984:I - 2007:III.The trend growth rate of the investment shock is chosen to matchthe average growth rate of the relative price of investment in the dataThe trend growth rate of the neutral shock is picked to match theobserved average growth rate of output per capitaTrend inflation is set at its observed value in each period.

Contribution of shocks to output growth volatility: MEI (50%),Neutral productivity (35%), Monetary policy (15%) followingJustiniano,Primiceri and Tambalotti (2010)


Calibration





Welfare costs

Mean consumption equivalent

Going from 0 to 4.75 percent and from 0 to 2.29 percent of trendinflation cause the welfare costs (in percent of consumption) to bearound:

in the baseline calibration : 8.38 and 2.34 respectively (see Table 5 )in the baseline calibration without trend growth : 4 and 0.137respectively (see Table 6 ).in the alternative calibration 13.56 and 2.37 respectively (see Table 7 )

Steady state consumption equivalent

Going from 0 to 4.75 percent and from 0 to 2.29 percent of trendinflation cause the welfare costs (in percent of consumption) to beabout :

in the baseline calibration 7.56 and 2.26 respectively (see Table 8 )in the baseline calibration without trend growth 3.57 and 0.123respectively (see Table 9 )in the alternative calibration 7.56 and 2.26 respectively (see Table 10 )


Welfare costs

Mean consumption equivalentGoing from 0 to 4.75 percent and from 0 to 2.29 percent of trendinflation cause the welfare costs (in percent of consumption) to bearound:






Welfare costs


in the baseline calibration : 8.38 and 2.34 respectively (see Table 5 )

in the baseline calibration without trend growth : 4 and 0.137respectively (see Table 6 ).in the alternative calibration 13.56 and 2.37 respectively (see Table 7 )





Welfare costs


in the baseline calibration : 8.38 and 2.34 respectively (see Table 5 )in the baseline calibration without trend growth : 4 and 0.137respectively (see Table 6 ).

in the alternative calibration 13.56 and 2.37 respectively (see Table 7 )Steady state consumption equivalent




Welfare costs







Welfare costs



Steady state consumption equivalentGoing from 0 to 4.75 percent and from 0 to 2.29 percent of trendinflation cause the welfare costs (in percent of consumption) to beabout :



Welfare costs




in the baseline calibration 7.56 and 2.26 respectively (see Table 8 )

in the baseline calibration without trend growth 3.57 and 0.123respectively (see Table 9 )in the alternative calibration 7.56 and 2.26 respectively (see Table 10 )


Welfare costs




in the baseline calibration 7.56 and 2.26 respectively (see Table 8 )in the baseline calibration without trend growth 3.57 and 0.123respectively (see Table 9 )

in the alternative calibration 7.56 and 2.26 respectively (see Table 10 )


Welfare costs






Volatilities

Unconditional volatilities

baseline calibration (see Table 11 )alternative calibration (see Table 12 )The decline in the volatility of inflation is larger than those experiencedby output and output output growth.

Conditional volatilities

baseline calibration

Output volatility (see Table 13 )Output growth volatility (see Table 14 )Inflation volatility (see Table 15 )

alternative calibration


Fluctuations in output volatility is accounted for by the N. shocks.interaction between trend inflation and MEI shocks is responsible forinflation volatility.Monetary shocks has a relatively larger contribution to the volatility ofoutput growth and its subsequent decline.


Volatilities

Unconditional volatilitiesbaseline calibration (see Table 11 )

alternative calibration (see Table 12 )The decline in the volatility of inflation is larger than those experiencedby output and output output growth.








Volatilities

Unconditional volatilitiesbaseline calibration (see Table 11 )alternative calibration (see Table 12 )

The decline in the volatility of inflation is larger than those experiencedby output and output output growth.








Volatilities

Unconditional volatilitiesbaseline calibration (see Table 11 )alternative calibration (see Table 12 )The decline in the volatility of inflation is larger than those experiencedby output and output output growth.








Volatilities


Conditional volatilitiesbaseline calibration






Volatilities



Output volatility (see Table 13 )

Output growth volatility (see Table 14 )Inflation volatility (see Table 15 )





Volatilities



Output volatility (see Table 13 )Output growth volatility (see Table 14 )

Inflation volatility (see Table 15 )alternative calibration




Volatilities








Volatilities




alternative calibrationOutput volatility (see Table 16 )

Output growth volatility (see Table 17 )Inflation volatility (see Table 18 )



Volatilities




alternative calibrationOutput volatility (see Table 16 )Output growth volatility (see Table 17 )

Inflation volatility (see Table 18 )Fluctuations in output volatility is accounted for by the N. shocks.interaction between trend inflation and MEI shocks is responsible forinflation volatility.Monetary shocks has a relatively larger contribution to the volatility ofoutput growth and its subsequent decline.


Volatilities




alternative calibrationOutput volatility (see Table 16 )Output growth volatility (see Table 17 )Inflation volatility (see Table 18 )



Volatilities





Fluctuations in output volatility is accounted for by the N. shocks.

interaction between trend inflation and MEI shocks is responsible forinflation volatility.Monetary shocks has a relatively larger contribution to the volatility ofoutput growth and its subsequent decline.


Volatilities





Fluctuations in output volatility is accounted for by the N. shocks.interaction between trend inflation and MEI shocks is responsible forinflation volatility.

Monetary shocks has a relatively larger contribution to the volatility ofoutput growth and its subsequent decline.


Volatilities







Impulse Responses Analysis

IRFs relative to baseline calibration, alternative calibration and atheoritical exercise (experiment) respectively.

Neutral (see Figure 1 , Figure 4 , Figure 7 )MEI (see Figure 2 , Figure 5 , Figure 8 )Monetary (see Figure 3 , Figure 6 , Figure 9 )

Neutral productivity shocks appear to be the main source ofcontribution to the volatility of output.Fluctuations in the inflation volatility are largely accounted for by MEIshocks by more than the neutral productivity shocks.Monetary shocks play an important role as the main explanation forthe volatility of output growth and its subsequent decline in thepost-1984 period.We find sources of the shift in macroeconomic variables volatilities :

changes in the Fed’s response to macroeconomic variables (or policyresponse to the shocks) (Clarida, Gali, and Gertler, 2000)along with the decline in trend inflation ( Coibion and Gorodnichenko,2011; Arias, Ascari, Branzoli and Castelnuovo, 2015).




Neutral (see Figure 1 , Figure 4 , Figure 7 )

MEI (see Figure 2 , Figure 5 , Figure 8 )Monetary (see Figure 3 , Figure 6 , Figure 9 )






Neutral (see Figure 1 , Figure 4 , Figure 7 )MEI (see Figure 2 , Figure 5 , Figure 8 )

Monetary (see Figure 3 , Figure 6 , Figure 9 )Neutral productivity shocks appear to be the main source ofcontribution to the volatility of output.Fluctuations in the inflation volatility are largely accounted for by MEIshocks by more than the neutral productivity shocks.Monetary shocks play an important role as the main explanation forthe volatility of output growth and its subsequent decline in thepost-1984 period.We find sources of the shift in macroeconomic variables volatilities :






Neutral productivity shocks appear to be the main source ofcontribution to the volatility of output.

Fluctuations in the inflation volatility are largely accounted for by MEIshocks by more than the neutral productivity shocks.Monetary shocks play an important role as the main explanation forthe volatility of output growth and its subsequent decline in thepost-1984 period.We find sources of the shift in macroeconomic variables volatilities :






Neutral productivity shocks appear to be the main source ofcontribution to the volatility of output.Fluctuations in the inflation volatility are largely accounted for by MEIshocks by more than the neutral productivity shocks.

Monetary shocks play an important role as the main explanation forthe volatility of output growth and its subsequent decline in thepost-1984 period.We find sources of the shift in macroeconomic variables volatilities :






Neutral productivity shocks appear to be the main source ofcontribution to the volatility of output.Fluctuations in the inflation volatility are largely accounted for by MEIshocks by more than the neutral productivity shocks.Monetary shocks play an important role as the main explanation forthe volatility of output growth and its subsequent decline in thepost-1984 period.

We find sources of the shift in macroeconomic variables volatilities :







changes in the Fed’s response to macroeconomic variables (or policyresponse to the shocks) (Clarida, Gali, and Gertler, 2000)

along with the decline in trend inflation ( Coibion and Gorodnichenko,2011; Arias, Ascari, Branzoli and Castelnuovo, 2015).


Conclusion

We have provided the implications of monetary policy changes on thewelfare in the U.S economy over the pre-1984 and post-1984 periods.

We find the main sources of the shift in macroeconomic variablesvolatilities.Our findings are consistent with the results in the literature relative tothe welfare costs over both sample periods.


Conclusion

We have provided the implications of monetary policy changes on thewelfare in the U.S economy over the pre-1984 and post-1984 periods.We find the main sources of the shift in macroeconomic variablesvolatilities.

Our findings are consistent with the results in the literature relative tothe welfare costs over both sample periods.


Conclusion

We have provided the implications of monetary policy changes on thewelfare in the U.S economy over the pre-1984 and post-1984 periods.We find the main sources of the shift in macroeconomic variablesvolatilities.Our findings are consistent with the results in the literature relative tothe welfare costs over both sample periods.


Appendix

Table: Non-Shock Parameters, Pre-1984

β δ α η χ b κ γ20.99 0.025 1/3 6 1 0.7 3 0.05θ σ ξp ξw φ ρi απ αy6 6 0.66 0.66 0.61 0.81 1.65 0.2

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Appendix

Table: Non-Shock Parameters, Post-1984

β δ α η χ b κ γ20.99 0.025 1/3 6 1 0.7 3 0.05θ σ ξp ξw φ ρi απ αy6 6 0.66 0.66 0.61 0.84 1.77 0.16

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Appendix

Table: Shock Parameters

Pre-1984gA gI ρr sr ρI sI ρA sA1.002581−φ 1.0029 0 0.002 0.81 0.0164 0.95 0.0033Post-1984gA gI ρr sr ρI sI ρA sA1.00191−φ 1.0065 0 0.001 0.81 0.0089 0.95 0.0018

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Appendix

Table: Alternative calibration

ρi απ αy sua suinvs sur

Before 1984 0.75 1.15 0.125 0.0028 0.0117 0.002After 1984 0.75 2.3 0.125 0.0016 0.0106 0.0019

We set ρI to 0.9 and double απ coefficent in the post-1984 whilemaintaining ρi and αy at their pre-1984 level;and shocks are computed accordingly.

Back


Appendix

Table: Consumption Equivalents, Mean

π∗ 1.00→Pre-19841.0000 01.0475 0.0838Post-19841.0000 01.0229 0.0234

Mean C.E based on the baseline calibrationBack


Appendix


π∗ 1.00→Pre-19841.0000 01.0475 0.040Post-19841.0000 01.0229 0.00137

Mean C.E based on the baseline calibration without trend growthBack


Appendix


π∗ 1.00→Pre-19841.0000 01.0475 0.1356Post-19841.0000 01.0229 0.0237

Mean C.E based on the alternative calibrationBack


Appendix

Table: Consumption Equivalents, Steady State

π∗ 1.00→Pre-19841.0000 01.0475 0.0756Post-19841.0000 01.0229 0.0226

Steady state C.E based on the baseline calibrationBack


Appendix


π∗ 1.00→Pre-19841.0000 01.0475 0.0357Post-19841.0000 01.0229 0.00123

Steady state C.E based on the baseline calibration without trendgrowth

Back


Appendix


π∗ 1.00→Pre-19841.0000 01.0475 0.0756Post-19841.0000 01.0229 0.0226

Steady state C.E based on the alternative calibrationBack


Appendix

Table: Unconditional volatilities

π∗ σ(Y ) σ(∆Y ) σ(π)

Pre-1984 1.0475 0.1084 0.0120 0.0032Post-1984 1.0229 0.0449 0.0064 0.0015Variation - -0.5859 -0.4676 -0.5409

Unconditional volatilities based on the baseline calibrationBack


Appendix

Table: Unconditional volatilities

π∗ σ(Y ) σ(∆Y ) σ(π)


Unconditional volatilities based on alternative calibrationBack


Appendix

Table: Output volatility

π∗ suinvs sua sur


Output volatilities based on baseline calibrationBack


Appendix

Table: Output growth volatility



Output growth volatilities based on baseline calibrationBack


Appendix

Table: Inflation volatility



Inflation volatilities based on baseline calibrationBack


Appendix

Table: Output volatility



Output volatilities based on alternative calibrationBack


Appendix

Table: Output growth volatility



Output growth volatilities based on alternative calibrationBack


Appendix

Table: Inflation volatility



Inflation volatilities based on alternative calibrationBack


Appendix

Figure: Neutral Shock

0 10 200

0.005

0.01

0.015

0.02output

0 10 20-10

-5

0

5x 10

-3 Hours

0 10 202

4

6

8

10

12

14x 10

-3Consumption

0 10 200

0.01

0.02

0.03

0.04Investment

0 10 20-0.01

-0.005

0

0.005

0.01

0.015Intermediate Input

0 10 200

0.002

0.004

0.006

0.008

0.01realwage

0 10 20-4

-2

0

2

4

6x 10

-3capital rental rate

0 10 20-6

-5

-4

-3

-2

-1

0x 10

-4nominal interest rate

0 10 20-5

-4

-3

-2

-1

0

1x 10

-3marginal cost

0 10 20-2

-1.5

-1

-0.5

0x 10

-3 inflation

0 10 200.005

0.01

0.015

0.02productivity

0 10 200

0.005

0.01

0.015

0.02Marginal Rate of Substitution

0 10 20-8

-6

-4

-2

0x 10

-3Wage Mark up

0 10 20-1

0

1

2

3

4

5x 10

-3Price Mark up

before 84after 84

IRFs relative to Neutral shock, based on the baseline calibrationBack


Appendix

Figure: MEI Shock

0 10 200

0.002

0.004

0.006

0.008

0.01

0.012output

0 10 20-2

0

2

4

6

8x 10

-3 Hours

0 10 200

2

4

6

8x 10

-3Consumption

0 10 200

0.01

0.02

0.03

0.04Investment

0 10 200

0.002

0.004

0.006

0.008


0 10 200.5

1

1.5

2

2.5

3x 10

-3 realwage

0 10 20-7

-6

-5

-4

-3

-2

-1x 10


0 10 20-4

-2

0

2

4

6

8x 10


0 10 20-1

-0.5

0

0.5

1x 10

-3marginal cost

0 10 20-2

0

2

4

6x 10

-4 inflation

0 10 201

2

3

4

5

6x 10

-3productivity

0 10 202

4

6

8

10x 10

-3Marginal Rate of Substitution

0 10 20-8

-6

-4

-2

0x 10

-3Wage Mark up

0 10 20-1

-0.5

0

0.5

1x 10

-3Price Mark up

before 84after 84

IRFs relative to MEI shock, based on the baseline calibrationBack


Appendix

Figure: Monetary Shock

0 10 200

0.5

1

1.5

2

2.5x 10

-3 output

0 10 20-5

0

5

10

15

20x 10

-4 Hours

0 10 204

6

8

10

12

14x 10

-4Consumption

0 10 200

1

2

3

4

5x 10

-3Investment

0 10 200

0.5

1

1.5

2

2.5x 10

-3Intermediate Input

0 10 201.5

2

2.5

3

3.5

4

4.5x 10

-4 realwage

0 10 20-5

0

5

10

15x 10


0 10 20-8

-6

-4

-2

0

2x 10


0 10 200

1

2

x 10-4marginal cost

0 10 20-1

0

1

2

3

4x 10

-4 inflation

0 10 202

3

4

5

6

7x 10

-4productivity

0 10 200

1

2

3

4

5x 10

-3Marginal Rate of Substitution

0 10 20-5

-4

-3

-2

-1

0x 10

-3Wage Mark up

0 10 20-3

-2.5

-2

-1.5

-1

-0.5

0x 10

-4Price Mark up

before 84after 84

IRFs relative to Monetary shock, based on the baseline calibrationBack


Appendix


0 5 10 15 200

0.005

0.01

0.015output

0 5 10 15 20-10

-5

0

5x 10

-3 Hours

0 5 10 15 200

0.005

0.01

0.015Consumption

0 5 10 15 200

0.005

0.01

0.015

0.02Investment

0 5 10 15 20-5

0

5

10x 10


0 5 10 15 200

2

4

6x 10

-3 realwage

0 5 10 15 20-2

0

2

4x 10


0 5 10 15 20-6

-4

-2

0x 10


0 5 10 15 20-3

-2

-1

0

1x 10

-3 marginal cost

0 5 10 15 20-15

-10

-5

0

5x 10

-4 inflation

0 5 10 15 204

6

8

10

12x 10

-3 productivity

0 5 10 15 200

0.005

0.01

0.015


0 5 10 15 20-0.015

-0.01

-0.005

0Wage Mark up

0 5 10 15 20-1

0

1

2

3x 10

-3 Price Mark up

before 84after 84

IRFs relative to Neutral shock, based on alternative calibrationBack


Appendix

Figure: MEI Shock

0 5 10 15 200

0.005

0.01

0.015output

0 5 10 15 200

2

4

6

8x 10

-3 Hours

0 5 10 15 200

0.005

0.01

0.015Consumption

0 5 10 15 200.005

0.01

0.015

0.02

0.025Investment

0 5 10 15 200

0.005

0.01


0 5 10 15 200

1

2

3

4x 10

-3 realwage

0 5 10 15 20-6

-4

-2

0

2x 10


0 5 10 15 20-5

0

5

10

15x 10


0 5 10 15 20-5

0

5

10x 10

-4 marginal cost

0 5 10 15 20-5

0

5

10

15x 10

-4 inflation

0 5 10 15 202

4

6

8x 10

-3 productivity

0 5 10 15 200

0.005

0.01

0.015


0 5 10 15 20-0.015

-0.01

-0.005

0Wage Mark up

0 5 10 15 20-10

-5

0

5x 10

-4 Price Mark up

before 84after 84

IRFs relative to MEI shock, based on alternative calibrationBack


Appendix


0 5 10 15 200

2

4

6x 10

-3 output

0 5 10 15 20-2

0

2

4

6x 10

-3 Hours

0 5 10 15 200

1

2

3

4x 10

-3 Consumption

0 5 10 15 200

0.005

0.01Investment

0 5 10 15 200

2

4

6x 10


0 5 10 15 202

4

6

8

10x 10

-4 realwage

0 5 10 15 20-1

0

1

2

3x 10


0 5 10 15 20-2

-1

0

1x 10


0 5 10 15 200

2

4

6x 10

-4 marginal cost

0 5 10 15 20-2

0

2

4

6x 10

-4 inflation

0 5 10 15 200

0.5

1

1.5x 10

-3 productivity

0 5 10 15 200

0.005

0.01


0 5 10 15 20-0.015

-0.01

-0.005

0Wage Mark up

0 5 10 15 20-6

-4

-2

0x 10

-4 Price Mark up

before 84after 84

IRFs relative to Monetary shock, based on alternative calibrationBack


Appendix


0 5 10 15 200

0.005

0.01

0.015output

0 5 10 15 20-10

-5

0

5x 10

-3 Hours

0 5 10 15 200

0.005

0.01

0.015Consumption

0 5 10 15 200

0.01

0.02

0.03Investment

0 5 10 15 20-5

0

5

10x 10


0 5 10 15 200

2

4

6

8x 10

-3 realwage

0 5 10 15 20-2

0

2

4x 10


0 5 10 15 20-8

-6

-4

-2

0x 10


0 5 10 15 20-3

-2

-1

0

1x 10

-3 marginal cost

0 5 10 15 20-15

-10

-5

0

5x 10

-4 inflation

0 5 10 15 204

6

8

10

12x 10

-3 productivity

0 5 10 15 200

0.005

0.01

0.015


0 5 10 15 20-0.015

-0.01

-0.005

0Wage Mark up

0 5 10 15 20-1

0

1

2

3x 10

-3 Price Mark up

before 84after 84B84 vs trendA84

IRFs relative to Neutral shock, based our theoritical exerciseBack


Appendix

Figure: MEI Shock

0 5 10 15 20

5

10

x 10-3 output

0 5 10 15 200

2

4

6

8x 10

-3 Hours

0 5 10 15 20-5

0

5

10

15x 10

-3 Consumption

0 5 10 15 200.005

0.01

0.015

0.02

0.025Investment

0 5 10 15 200

0.005

0.01


0 5 10 15 200

1

2

3

4x 10

-3 realwage

0 5 10 15 20-6

-4

-2

0

2x 10


0 5 10 15 20-5

0

5

10

15x 10


0 5 10 15 20-5

0

5

10x 10

-4 marginal cost

0 5 10 15 20-5

0

5

10

15x 10

-4 inflation

0 5 10 15 202

3

4

5

6x 10

-3 productivity

0 5 10 15 200

0.005

0.01

0.015


0 5 10 15 20-15

-10

-5

0

5x 10

-3 Wage Mark up

0 5 10 15 20-10

-5

0

5x 10

-4 Price Mark up


IRFs relative to MEI shocks, based our theoritical exerciseBack


Appendix


0 5 10 15 200

2

4

6x 10

-3 output

0 5 10 15 20-2

0

2

4

6x 10

-3 Hours

0 5 10 15 200

1

2

3

4x 10

-3 Consumption

0 5 10 15 200

0.005

0.01Investment

0 5 10 15 200

2

4

6x 10


0 5 10 15 202

4

6

8

10x 10

-4 realwage

0 5 10 15 20-1

0

1

2

3x 10


0 5 10 15 20-2

-1

0

1x 10


0 5 10 15 200

2

4

6x 10

-4 marginal cost

0 5 10 15 20-2

0

2

4

6x 10

-4 inflation

0 5 10 15 200

0.5

1

1.5x 10

-3 productivity

0 5 10 15 200

0.005

0.01


0 5 10 15 20-0.015

-0.01

-0.005

0Wage Mark up

0 5 10 15 20-6

-4

-2

0x 10

-4 Price Mark up


IRFs relative to Monetary shock, based our theoritical exerciseBack


on the welfare costs of monetary policy

Economy & Finance