The Keynesian multiplier, news and fiscal policy rules in a DSGE model … · 2012-09-20 · Model of the Keynesian multiplier: To re-instate the multiplier via the effect of news

The Keynesian multiplier, news and fiscal policy rules in a DSGE model

Authors:

George Perendia and Chris Tsoukis

[email protected] [email protected]

London Metropolitan University

mailto:[email protected]


Abstract:

• We extend the standard Smets-Wouters (2007) medium-

sized DSGE model in two directions, namely to analyse

the effects of news and the Keynesian multiplier, and

secondly to incorporate a fiscal policy rule.

• We show that both the news channel and the government

spending fiscal policy rule significantly improve model fit to

data. We then simulate the effects of monetary and of fiscal

policy and particularly the role of the Keynesian vs. the

neoclassical aspects of the model in driving the results.

Motivation

Fiscal policy is again rising to prominence because:

• Limited effectiveness of monetary policy (zero bound effects, etc);

• In Europe, because of the loss of monetary sovereignty.

But debate continues to surround the desirability and effectiveness of fiscal policy and the controversy surrounding the „Obama stimulus plan‟, the ARRA 2009*.

• particularly government spending,

• crystallised around the notion of the „Keynesian multiplier‟, the notion of a virtuous circle of government spending generating incomes-consumption-output-further incomes, etc.,...

• both providing a rationale for fiscal policy via government spending.

*) American Recovery and Reinvestment Act, 2009

Introduction – the multiplier (I):

Two strands in the static multiplier literature:

1) a static variety of models seeks to re-discover the

Keynesian multiplier in static monopolistic set-up.

The balanced-budget multiplier emerges in the short

run because of the virtuous circle:

higher spending generating higher company profits

then feed on to higher spending

the multiplier vanishes in the long run because free

entry eliminates all profits and breaks the virtuous

circle.

(Mankiw, 1988; Starz, 1989; Dixon, 1987; Dixon and Lawler, 1996;

Heijdra, 1998, Heijdra, Ligthart and van der Ploeg, 1998;

Sylvestre, 1993;)

Introduction – the multiplier (II):

• 2) A second static strand of literature is purely neoclassical

(Hall, 2009, Woodford, 2011, Mulligan, 2011):

• Rational agents realise that government spending increases

will be accompanied by tax increases;

• Hence (rational consumer‟s) consumption declines

(„crowded out‟);

• Output rises because a poorer consumer will work harder

(will „buy less leisure‟);

• But the output rises is less than the government spending

increase.

• Neoclassical conclusions are vigorously contested by the

latest of Summers and DeLong (2012).

Introduction – the multiplier (III):

A 3rd strand builds on (Neoclassical) intertemporal

optimisation

include response of consumption to changing interest rates,

integrating fiscal policy with dynamic macroeconomics.

But due to their diversity they

fail to reach uniform conclusions; e.g. on,

the magnitudes of short- relative to long-run multipliers,

and

whether or not private consumption is crowded out or in

Mostly share with the static approaches the weakness that

fiscal policy is entirely wasteful!

(Aschauer, 1985, 1988; Barro, 1989; Aiyagari et al., 1990; Christiano and

Eichenbaum, 1992; Baxter and King, 1993; Gali, Lopez-Salido and

Valles, 2002)

Introduction:

This paper seeks to enhance our understanding of of fiscal policy

in the context of the

business cycles and current crisis, and

its potential for stabilisation.

we utilise a standard medium-sized DSGE model as in Smets

and Wouters (2007) (see also Drautzburg and Uhlig, 2010).

Our innovation is twofold,

to incorporate a Keynesian multiplier along the lines of the

first strand of literature summarised above; and

to account for fiscal policy that is not a random exogenous

shock as usually modelled, but, instead:

– may be endogenous, and,

– may follow a fiscal policy rules akin to that of Taylor

(1993) monetary policy rule.

Model of the Keynesian multiplier:

To introduce the Keynesian multiplier, we employ a variant

of the Euler equation for consumption that accounts for

unexpected developments in output and the interest rate

(„news‟).

Unexpected developments then adds up to output via

national income accounting, and then

further affects consumption due to our formulation of

consumption with the news.

a Keynesian multiplier structure arises around the

backbone of intertemporal evolution of the Euler

equation.

Such a structure is absent in standard formulations,

hampering a better understanding of the workings of

fiscal policy.


The standard Euler equation shows the time profile of

consumption and its response to incentives to save (the

real interest rate) or consume now (rate of time

preference);

it is silent on how consumption responds to changes in

lifetime resources.

it takes into consideration the anticipated lifetime

resources at the beginning of the planning period,

but

any subsequent revisions of those are not reflected in the

path of consumption.

Schematically, the Euler equation determines the slope of the

consumption profile but not its position – see next slide.

Consumption profile over the lifetime

Figure 1: Consumption and „news‟

logC

to t1 t

Model of the Keynesian multiplier:In above figure

the bold consumption profile is determined at t0.

Euler eq. determines the slope – can change at any time.

But, its position is determined only once, at t0 (and

implicitly), reflecting the lifetime resources anticipated

then.

However, if at t1, say, there is „news‟, a revision of

lifetime fortunes (unanticipated at t0) that might warrant

a shift to a higher profile with the same slope (thinner

line), this development will be lost in the Euler equation.

This is a crucial omission, as at the core of the multiplier

is the virtuous circle fiscal expansion – higher incomes

over the lifetime – higher consumption – higher output

and lifetime incomes, etc.

(see Starz, Mankiw, and Dixon and others);


Naturally, all estimable Euler equations contain error

terms, which may be interpreted as news about future

resources (among other things),

but

these are entirely exogenous and random, hence

unrelated to the logic of the multiplier above.

One may say that the interest rate also reflect the „news‟,

but

this channel is much too indirect and uncertain to

support a Keynesian multiplier.

Model of the Keynesian multiplier:To re-instate the multiplier via the effect of news onconsumption, we adopt a variant of the „permanentincome theory of consumption‟, following Obstfeld andRogoff (1996, Ch. 2, equation 2.16).

(1)

Where

,

is the inverse of the discount factor,

At current wealth.

Xt is labour earnings plus monopoly profits, and linearisation gives eq. (2):

0

/)1(~1

~

s

s

tstttt RXEAr

rC

s

v

vt

s

t rR1

)~1(

0

11

0 )~1(

)~1/()1)(1(~1

1

)~1(

)1(~1

~

ss

ststt

ss

stttt

r

yrrE

rr

xEa

r

r

C

Xc


Following Deaton (1990, Ch. 3), we use the period budget

constraint in a beginning-of-period formulation in a

linearised form (eq 3‟):

and supplementing (3‟) into the consumption equation (2):

ttttt rcA

Cx

A

Xara )1()1()~1( 111

0

11

0

111

)~1(

)~1/()1)(1(

1

1

)~1(

)1(

)1()1()~1(

~1

~

ss

ststt

ss

stt

tttt

t

r

yrrE

rr

xE

rcA

Cx

A

Xar

r

r

C

Xc

If we lag (2) and multiply result by (1+r-) and subtract

from (4), we get (5):

Where

• The key is that the evolution of consumption isattributed to „news‟, i.e, revisions of expectations due tothe shocks hitting the system.

• The relation to the multiplier is that when outputchanges, so will profits and labour earnings, and

• this will create „news‟ of higher future earnings,


0

111

0

1

)~1(

)1/()~1/()1()(

~1

)1/()~1/()1(

)~1(

)1)(()1(

~1

~

ss

ststtt

tt

ss

stttt

t

r

yrrEE

r

yrr

r

xEEr

r

r

Cc

sttsttsttt xExExEE 11)(

To close the model, we need:

(6)

where Mt: Real monopolistic (“supernormal”) profits,

in linearised form:

(6‟)

Introducing (6‟) into (5) we get consumption difference (7a)

and present value of labour earnings+monopoly profits Wt:

(7b)

whose revision in expectations form the news effect.


))1/(11()/1( ttttttttt

M

tttt mYLWPMCYLWLWX

p

ttttt lwlshareyx )(

W

r

yrrEEr

r

r

Cc tt

ttttt ~1

)1/()~1/()1()()1(~1

~

1

)1()~1(

)1()1(~1

111

WW tt

tt

t

y

r

rx

r

Fiscal policy and (un-)employment targeting rules

Our second innovation concerns the fiscal policy rule a la

Taylor (1993). I.e. we explicitly recognise that:

fiscal policy is NOT random exogenous shock as wouldhave been modelled customary, and,

it shows endogenous association with the business cycle.

We tested several models based on S&W 2007 model‟sexogenous spending equation but with variations of thenews and/or unemployment* (or the lag-differences ofunemployment or labour force) added on the lines of:

or

*)when if used, the unemployment at time t was defined as adifference between the flexible (frictionless) and the rigideconomy‟s labour forces: ut = lf,t - lt

atygtttutgt guuggg )( 11

atygttttttutgt gEEuuggg W )()( 111

Models:

As a benchmark we used Dynare estimation results of

S&W‟07 model with the original US data and its Log data

density* which is estimated to be -925.087641

M0: A standard Euler equation as in SW, with no news in

either the Euler equation SW or the government spending

„Taylor rule‟, but with the unemployment rate (lagged

difference) defined as above.

We achieved the estimated Log-Density* of -917 , i.e.

substantially higher than for the original S&W 07 model!

*) We used Dynare for estimation of all models to Log data density

[Laplace approximation] stage only at this stage of research.

Models:

M1: Backward looking consumption with news; a

government spending „Taylor rule‟ with news effect:

this model failed the Blanchard-Kahn (1980) test due to

an insufficient number of forward looking variables

tttttt EEcc W )( 11 ,)1()~1(

)1()1(~1

111

WW tt

t

t

t

y

r

rx

r

atygtttttutgt gEEuggg W )( 11

Models:

M2: A standard Euler equation combined with Model 1,

with two types of mutually exclusive (weighted)

heterogeneous agents, one that follow the, the standard

S&W NK forward looking consumption expectation and

the other, backward looking but with the news effect:

This model achieved estimated log-density -915

A similar model but with the forward looking

unemployment difference in the fiscal rule:

achieved even better fit to data with log-density -912!

ttt ccc 21)1( , 10

)()()1( 3121111111 bttttttttt rclElccEcc

tttttt EEcc W )( 11222 ,)1()~1(

)1()1(~1

111

WW tt

t

t

t

y

r

rx

r

atygtttttutgt gEEuggg W )( 11


Models:

M3: An (SW07) Euler equation with news added, and a

basic government spending rule (I.e. without news or

unemployment targeting rule):

Estimated LDD= -929.6 (which is worse than SW07‟s)

M 4: A standard Euler equation (identical to SW), with a

government spending rule featuring news but no

unemployment targeting rule:

The estimated LDD= -912.1 is indicating importance of

endogenising so called “exogenous” government spending.

)()()()1( 312111 btttttttttttt rclElcEEcEcc W

atygttgt ggg 1

atygtttttgt gEEgg W )( 11

Models:

M5: As Model 4 with the addition of the change in the

unemployment rate in the government spending rule, as

follows:

(usmodel_li1KM01_wgdu.mod ) Estimated LDD=-911.9.

M 6: As model 3 (Euler equation with news) with the

addition of news (but no unemployment) in the fiscal

„Taylor rule‟:

This effectively augments both the Euler equation and the

fiscal rule with news. Estimated LDD=-912.



atygtttttgt gEEgg W )( 11

Models:

M 7: As Model 6 with the addition of the forward-looking

difference in unemployment in the fiscal rule:

Estimated LDD=-911.9

M8: As in model 7 Euler with backward-looking (instead

of forward-looking) change in unemployment in the fiscal

rule:

Estimated LDD=-912.3; estimated 0.4395.





Models:

M 9: As in models 8 and 9 with the simple unemployment

rate (instead of its difference) in the fiscal unemployment

targeting rule:

Estimated LDD=-911.5, 0.45

M 11: As in model 9 but with backward-looking change in

labour force instead of unemployment in the fiscal rule:

Estimated LDD=-910.5;

M 12: A similar model but with no news in either Euler or

fiscal rule but only labour difference gives LLD=-913.1



atygttttttutgt gEEllggg W )()( 111

Results:Multiplier Fiscal policy

Rank Model

news

in c

news

in g

(un)emp

rule

used

unempl

oyment

params LDD

MCMC

10000 Note

1 11 0.1463 -0.26 lab bk dif -0.1732 -910.513

2 9 0.1634 -0.298 simple u 0.0265 -911.493

3 7 0.151 -0.281 u fwd dif 0.164 -911.918

4 5 -0.259 u bk dif 0.1592 -911.926

5 6 0.1569 -0.295 -912.057

6 4 -0.316 -912.079

7 8 0.1544 -0.265 u bk dif 0.1154 -912.331

8 10 0.269 -0.261 simple u 0.0257 -912.352 Heterogen agents

9 12 lab bk dif -0.4711 -913.115 -917.586

10 2 0.4602 -0.318 simple u 0.0218 -915.805 Heterogen agents

11 0 u bk dif 0.4802 -917.623 -921.946

12 SW1 -924.956 -929.036 SW 07 li1

13 SW2 -925.088 -929.985

SW 07 li2,

ORIGINAL

14 3 -0.024 -929.619

Original S&W 2007 model responses to hg shock to g (I.e. g)

Results:

5 10 15 20-1

0

1dy

5 10 15 200

0.5

1y

5 10 15 200

0.01

0.02pinfobs

5 10 15 200

0.02

0.04robs

5 10 15 20-0.4

-0.2

0c

5 10 15 20-0.05

0

0.05w

5 10 15 200

0.2

0.4lab

5 10 15 200

0.5

1g

5 10 15 20-1

-0.5

0inve

Results:

The employment difference based fiscal rule only model 12 responses to

hg shock to g (I.e. g)

News and fiscal rule model 11 responses to hg shock to g (I.e. g)

Results:

Results (I):

• Experimenting with the models and data in the “linear

space” experimental laboratory of DSGE models

estimation and simulation Dynare toolkit, we found that

• our model behaves in a comparable manner to SW07.

• Having, however, with a sizeably higher likelihood, our

models provide a much better fit to data than SW07.

• Our estimation results show dramatic improvements

when either one or both factors,

– the news, and/or

– the (un-) employment

targeting rules are added to the so called “exogenous”

(government) spending and making it more endogenous.

The Multipliers

• Textbook multiplier: (Yt-Y0)/dG0

• 2 adjustments to render meaningful:

• As raw IRF of consumption gives a deviation of c from

its trend as a % of C, we multiply by the mean

consumption-output ratio (0.6) to express deviations as

% of output;

• Question over „true‟ exogeneity: In our model it is the

shock (eg) but if government have a target of g, then the

latter may be thought of as the exogenous variable with

eg as residual (endogenous) adjustment – hence, take

either as the true fiscal impulse.

The Multipliers – Table 2

Table 2 presents the following multipliers:

The models are organised in pairs, where, in each pair,

• Model a is the version with news in the Euler equation,

• Model b is the version of the same model without news*

*) Models 2a and 2b are not exact counterparts, in this respect, as 2a has

unemployment in the fiscal rule, whereas 2b has the difference in

unemployment in the fiscal rule; otherwise, they are exact counterparts,

except that 2a has news in the Euler equation whereas 2b does not.)

Table 2 – part i.

Quarter after shock

0 1 2 3 4 5 6 7 11 15 19

1a. usmodel_li1KM01_wswgdl_1_ news in SW+ g + lab diff in g LDD -910 BEST of all

c_eg/eg 0.16 0.10 0.05 0.01 -0.03 -0.05 -0.08 -0.10 -0.14 -0.16 -0.17

y_eg/eg 0.80 0.69 0.60 0.53 0.47 0.41 0.37 0.33 0.23 0.18 0.15

g_eg/eg 0.60 0.60 0.59 0.59 0.58 0.57 0.56 0.55 0.51 0.46 0.42

c_eg/g0 0.26 0.17 0.08 0.01 -0.04 -0.09 -0.13 -0.16 -0.24 -0.27 -0.28

y_eg/g0 1.34 1.16 1.01 0.88 0.78 0.69 0.61 0.55 0.39 0.30 0.24

g_eg/g0 1.00 1.00 0.99 0.98 0.97 0.95 0.94 0.92 0.84 0.77 0.69

1b. usmodel_lik1_gl_1 no news only diff lab in g LDD -913

c_eg/eg -0.03 -0.07 -0.10 -0.12 -0.14 -0.16 -0.17 -0.18 -0.20 -0.21 -0.20

y_eg/eg 0.74 0.66 0.59 0.54 0.48 0.44 0.40 0.37 0.27 0.21 0.17

g_eg/eg 0.74 0.74 0.74 0.74 0.73 0.72 0.71 0.70 0.63 0.57 0.51

c_eg/g0 -0.05 -0.09 -0.13 -0.16 -0.19 -0.21 -0.23 -0.24 -0.27 -0.28 -0.27

y_eg/g0 0.99 0.89 0.80 0.72 0.65 0.59 0.54 0.49 0.36 0.28 0.22

g_eg/g0 1.00 1.00 1.00 1.00 0.99 0.97 0.96 0.94 0.86 0.77 0.68

Table 2 – part ii.

Quarter after shock

0 1 2 3 4 5 6 7 11 15 19

2a. usmodel_li1KM01_swcy1gu_w1_rc1pi2_ news in SW+ g + u in g LL911 BEST with unemployment

c_eg/eg 0.20 0.14 0.09 0.05 0.01 -0.02 -0.05 -0.07 -0.13 -0.15 -0.16

y_eg/eg 0.86 0.72 0.60 0.51 0.43 0.36 0.30 0.26 0.15 0.09 0.07

g_eg/eg 0.62 0.60 0.57 0.55 0.53 0.51 0.49 0.48 0.42 0.37 0.33

c_eg/g0 0.33 0.23 0.15 0.08 0.02 -0.03 -0.07 -0.11 -0.20 -0.24 -0.26

y_eg/g0 1.39 1.16 0.97 0.81 0.68 0.58 0.49 0.42 0.24 0.15 0.11

g_eg/g0 1.00 0.96 0.92 0.88 0.85 0.82 0.79 0.76 0.67 0.59 0.52

2b. usmodel_li1KM01_wgdu _no news in SW but news and du in g 911.9

c_eg/eg -0.02 -0.05 -0.07 -0.09 -0.11 -0.12 -0.13 -0.14 -0.16 -0.16 -0.16

y_eg/eg 0.73 0.64 0.56 0.49 0.44 0.39 0.35 0.32 0.23 0.18 0.14

g_eg/eg 0.72 0.70 0.67 0.66 0.64 0.62 0.60 0.59 0.52 0.46 0.41

c_eg/g0 -0.03 -0.07 -0.10 -0.13 -0.15 -0.17 -0.19 -0.20 -0.22 -0.22 -0.22

y_eg/g0 1.02 0.89 0.78 0.68 0.61 0.54 0.49 0.45 0.32 0.25 0.20

g_eg/g0 1.00 0.96 0.93 0.91 0.88 0.86 0.84 0.82 0.73 0.64 0.57

Table 2 – Model 1a: responses normalised by eg0

Table 2 – Model 1a : responses normalised by g0

Multipliers – cont’d.

• Furthermore, the numerator of the multiplier, (Yt-Y0)/dG0,

can be decomposed as change along the trend plus

deviation from it;

• Only latter should be considered:

• Trend is completely exogenous, unrelated to fiscal

policy (as that is not assumed productive);

• Trend explodes asymptotically;

• Hence, if output devs. (in levels) is and

it follows that .

• Table 3 presents

Table 3

Quarter after shock

0 1 2 3 4 5 6 7 11 15 19

1a. usmodel_li1KM01_wswgdl_1_ news in SW+ g + lab diff in g LDD -910 BEST of all

c_eg/eg 0.16 0.10 0.05 0.01 -0.03 -0.06 -0.08 -0.10 -0.15 -0.17 -0.18

y_eg/eg 0.80 0.70 0.61 0.54 0.47 0.42 0.38 0.34 0.24 0.19 0.16

g_eg/eg 0.60 0.60 0.60 0.60 0.59 0.58 0.58 0.57 0.53 0.49 0.45

c_eg/g0 0.26 0.17 0.08 0.01 -0.04 -0.09 -0.13 -0.17 -0.25 -0.29 -0.31

y_eg/g0 1.34 1.16 1.02 0.89 0.79 0.70 0.63 0.57 0.41 0.32 0.26

g_eg/g0 1.00 1.00 1.00 0.99 0.98 0.97 0.96 0.95 0.88 0.82 0.75

1b. usmodel_lik1_gl_1 no news only diff lab in g LDD -913

c_eg/eg -0.03 -0.07 -0.10 -0.12 -0.14 -0.16 -0.18 -0.19 -0.21 -0.22 -0.22

y_eg/eg 0.74 0.67 0.60 0.54 0.49 0.45 0.41 0.38 0.28 0.22 0.18

g_eg/eg 0.74 0.75 0.75 0.75 0.75 0.74 0.73 0.72 0.67 0.61 0.55

c_eg/g0 -0.05 -0.09 -0.13 -0.17 -0.20 -0.22 -0.24 -0.25 -0.28 -0.30 -0.30

y_eg/g0 0.99 0.90 0.81 0.73 0.66 0.60 0.55 0.51 0.38 0.30 0.24

g_eg/g0 1.00 1.01 1.01 1.01 1.00 0.99 0.98 0.97 0.90 0.82 0.74

Table 3 – Model a: responses normalised by eg0

Table 3 – Model a: responses normalised by g0

Results (II):

1. Models with news in the Euler equation consistently

show higher responses of both consumption and output

to the fiscal shock.

2. Choice of the scaling factor (one standard deviation of

the estimated exogenous spending shock or g0) matters a

lot. In the latter case, we get true Keynesian multipliers

of higher than unity, that last at least for a year.

3. Incorporation of news is also critical in the sense that,

with it, consumption responds positively to the fiscal

shock in both types of shock (eg0 and g0), whereas

4. without it, the consumption response is lower, and

negative in the case of the former type of shock.

This refutes the key criticism of the fiscal multiplier that it

crowds out private consumption (if it actually does)

view (see e.g. Barro, 2010)

This paper seeks to enhance our understanding of fiscal policy in

the context of the

business cycles and current crisis, and

its potential for stabilisation.

We utilise a standard medium-sized DSGE model as in Smets

and Wouters (2007) (see also Drautzburg and Uhlig, 2010).

Our innovation is twofold,

to incorporate a Keynesian multiplier by allowing for „news‟

(unexpected revisions in lifetime wealth) to augment the

Euler equation, hence giving rise to an output news –

consumption – further output changes virtuous circle; and

to account for the evolution of fiscal policy that is not random

and exogenous, but may follow a rule akin to that of Taylor

(1993) for monetary policy.

Conclusions (I):

Conclusions (II):

• Another (New) Keynesian feature is inclusion of change

of employment rates or of unemployment (as difference

between the employment rates of the actual and flexible-

price economy) that affects the fiscal policy rule.

• More neo-classical features include

– intertemporal optimisation,

– elastic labour supply,

– trend growth.

• Our results show dramatic improvements in estimationresults over the standard SW specification.

The „news‟ channel allows for a change in resultstowards a more „keynesian‟ flavour – more prolongedoutput responses, positive consumption responses.

Possible extensions in future work:

• Extend the model towards heterogeneous framework, e.g. add the non-Ricardian consumers a la Drautzburg and Uhlig,

• optimistic and pessimistic (Animal spirit driven) agents along the lines of DeGrauwe, (2009) and

• the imperfect (partial) information solution framework with the adaptive behaving agents on the lines of Levine, Pearlman, Perendia and Yung (2010).

• Allow for beneficial effects of public debt on growth (e.g., Traum and Yang, 2009) – e.g., due to a possible reduction in capital gains taxes or increase in business investment.

• Allow for special nature of government spending:

• production-enhancing, e.g. via infrastructure-building;

• related to defence (see papers by Barro).

Thank you for listening!

The Keynesian multiplier, news and fiscal policy rules in a DSGE model

Authors:

George Perendia and Dr Chris [email protected] [email protected]

London Metropolitan University



Documents

The Keynesian multiplier, news and fiscal policy rules in a DSGE model … · 2012-09-20 · Model of the Keynesian multiplier: To re-instate the multiplier via the effect of news