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Intro ducti on
Mod els
Resul ts
Conc lusion
Central bank losses and monetary policy
rules: a DSGE investigation
Western Economic Association International
Keio University, Tokyo, 21-24 March 2019.
Jonathan Benchimol1and André Fourçans2
This pre sentat ion do es not ne cessaril y re‡ect the view s of the B ank of Isr ael
March 21, 2019
1Bank of Israel
2ESSEC Business School and THEMA
Jonat han Ben chimo l ESSE C Busin ess Sch ool and T HEM A
Intro ducti on
Mod els
Resul ts
Conc lusion
Ques tions
Litera ture
Findi ngs
The issues
IRules vs discretion in monetary policy. Rules for academics,
uncertain for policy makers.
IDebates held during the 70s-80s put forward more or less
nominal income targeting concepts, even if they were not
presented as such.3
IThe consensus with respect to Taylor (1993) rules increased
during the last two decades.4
ICriticism towards such Taylor-type rules also increased,5
especially over the GFC.6
ICould nominal income targeting be a better way to achieve
the central banks’objectives ?
3Friedman, 1971; Meade, 1978; McCallum, 1973, 1987.
4Bernanke & Mishkin, 1997; Svensson, 1999; Taylor, 1999.
5Hall & Mankiw, 1994; Frankel & Chinn, 1995; McCallum and Nelson, 1999.
6Hendrickson, 2012; Woodford, 2012; Frankel, 2014; Sumner, 2014, 2015;
McCallum, 2015.
2 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Ques tions
Litera ture
Findi ngs
Research Issues
In it’s post "MacroMania on Nominal GDP Targeting and the
Taylor Rule", John Taylor suggested that:7
Idi¤erent monetary proposals and rules "should be compared
and evaluated".
Ito simulate them in macro models "hopefully dynamic
stochastic models" is "a good way to compare and evaluate
di¤erent monetary proposals and rules".
I"the dynamics are so important and so hard to work through
intuitively, empirical models can help a lot".
I"more policy evaluation research on the new and di¤erent
proposals is needed to inform the policy discussion, and it is
certainly welcome in my view".
7EconomicsOne.com, Sept. 8, 2013.
3 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Ques tions
Litera ture
Findi ngs
Literature review
IMeade, 1978. The meaning of internal balance. Economic
Journal.
ITaylor, 1993. Discretion versus policy rules in practice.
Carnegie-Rochester Conference Series on Public Policy.
IFrankel and Chinn, 1995. The stabilizing properties of a
nominal GNP rule. Journal of Money, Credit and Banking.
IRudebusch, 2002. Assessing nominal income rules for
monetary policy with model and data uncertainty.
Economic Journal.
ISmets and Wouters, 2007. Shocks and frictions in US
business cycles: a Bayesian DSGE approach. American
Economic Review.
IGalí, 2015. Monetary policy, in‡ation and the business
cycle: an introduction to the New Keynesian framework.
Princeton University Press.
4 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Ques tions
Litera ture
Findi ngs
What do we do ?
IEvaluate various monetary rules and their consequences in
terms of CBs’objectives.
IUse of canonical SW2007 New-Keynesian DSGE model …tted
to the US.
IEmpirical analysis of 12 rules (4 Taylor type, 4 NGDP growth
type, 4 NGDP level type).
IBayesian estimations over 1955-2017 and various subsamples.
I3 subsamples with di¤erent environments and monetary policy
styles:
I1955-1985;
I1985-2007;
I2007-2017.
IEstimations and analysis of models leading to:
Imonetary rules parameters;
Iin-sample …ts;
ICB’s loss function (current and forecasted). 5 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
Smets and Wouters (2007) in a nutshell
ISticky and ‡exible-price economy.
IHouseholds, …rms, and central bank blocks.
Isticky-prices and wages.
ICapital and investment features.
IRich stochastic structure: technology, monetary policy,
markups (wages and prices), risk premium, investment, and
government spending.
IOne ad-hoc monetary policy rule.
7 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
Models Sources
1Smets and Wouters (2007)
2Taylor (1993)
3Gali (2015)
4Garin,Lester, and Sims (2016)
5Adapted NGDP Growth Targeting
6NGDP Growth + FPC Targeting
7NGDP Growth + NIR Targeting
8NGDP Growth Targeting
9Adapted NGDP Level Targeting
10 NGDP Level + FPC Targeting
11 NGDP Level + NIR Targeting
12 NGDP Level Targeting
8 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
1: rt=ρrt1+(1ρ) [rππt+ry(ytyp
t)] +r4y(4yt 4yp
t)+εr
t
2: rt=ρrt1+(1ρ) [rππt+ry(ytyp
t)] +εr
t
3: rt=ρrt1+(1ρ) [r
t+rππt+ry(ytyp
t)] +εr
t
4: rt=ρrt1+(1ρ) [rππt+ry4yt]+εr
t
5: rt=ρrt1+(1ρ) [rn(πt+4yt 4yp
t)] +r4y(4yt 4yp
t)+εr
t
6: rt=ρrt1+(1ρ) [rn(πt+4yt 4yp
t)] +εr
t
7: rt=ρrt1+(1ρ) [r
t+rn(πt+4yt 4yp
t)] +εr
t
8: rt=ρrt1+(1ρ) [rn(πt+4yt)] +εr
t
9: rt=ρrt1+(1ρ) [rn(pt+ytyp
t)] +r4y(4yt 4yp
t)+εr
t
10: rt=ρrt1+(1ρ) [rn(pt+ytyp
t)] +εr
t
11: rt=ρrt1+(1ρ) [r
t+rn(pt+ytyp
t)] +εr
t
12: rt=ρrt1+(1ρ) [rn(pt+yt)] +εr
t
9 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
Why these rules?
IOur Taylor-type rules are based on:
IRule 1: Rule 2 + output-gap growth component
4yt 4yp
t.
IRule 2: Taylor (1993) with a microfounded output gap
ytyp
t.
IRule 3: Rule 2 with a natural interest rate component (r
t).
IRule 4: a GDP growth targeting without ‡exible-price
economy unknowns (NIR and FPC).
IOur NGDP Growth rules replace the core functions of the
previous rules with a NGDP growth targeting function (rules 5
to 8).
IOur NGDP Level rules replace the core functions of the
previous rules with a NGDP level targeting function (rules 9
to 12).
10 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
Data
IAs in Smets-Wouters (2007), we use the following time series
extracted from FRED R
:
IReal Gross Domestic Product.
IImplicit Price De‡ator.
IPersonal Consumption Expenditures.
IFixed Private Investment.
ICivilian Employment.
ICivilian Non institutional Population.
IAverage Weekly Hours from Nonfarm Business Sector.
ICompensation Per Hour from Nonfarm Business Sector.
IE¤ective Federal Funds Rate.
IWu-Xia (2016) shadow rate from 2009Q2 to 2015Q4; Fed
funds otherwise.
IFor each sample, we use the same data-transformations as in
Smets-Wouters (2007).
11 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Smet s and Wou ters (20 07)
Mone tary pol icy rules
Expla nation s
Samples
For each model, estimations are done over 4 di¤erent periods:
IFull sample: 1955 – 2017.
IGFC/ZLB era: 2007 – 2017.
IDiscretionary era: 1955 – 1985.
IGM era: 1985 –2007.
Our estimation procedures are in line with the DSGE-Bayesian
estimation literature (Smets and Wouters, 2007; An and
Schorfheide, 2007).
12 / 27
1955-2017
1 2 3 4 5 6 7 8 9 101112
0
0.5
12007-2017
1 2 3 4 5 6 7 8 9 101112
0
0.5
11985-2007
1 2 3 4 5 6 7 8 9 101112
0
0.5
11955-1985
1 2 3 4 5 6 7 8 9 101112
0
0.5
1
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
1 2 3 4 5 6 7 8 9 101112
0
1
2
Monetary policy rule parameter values for each model (1 to 12).
Intro ducti on
Mod els
Resul ts
Conc lusion
Parame ters and …tting
Asses sment
In-sample …t
Sample Rule
1 2 3 4 5 6 7 8 9 10 11 12
1955-2017 -1491 -1515 -1512 -1510 -1464* -1481 -1488 -1514 -1563 -1602 -1556 -1548
2007-2017 -269 -270 -285 -285 -307 -308 -283 -302 -258 -262 -278 -254*
1985-2007 -386 -428 -408 -406 -406 -404 -396 -410 -393 -395 -405 -383*
1955-1985 -817* -824 -835 -840 -840 -855 -837 -842 -844 -846 -863 -853
Table: Log marginal data densities for each model and each period
(Laplace approximation). * indicates the best value for each period.
IFor each period a di¤erent rule, but rule 12 twice.
ISuggests that the Fed may have changed strategy during the
GM compared to before 1985, from Taylor type to NGDP
level targeting.
15 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Parame ters and …tting
Asses sment
Central bank’s loss
IOur general central bank loss function is de…ned such as
Lt=var (πt)+λyvar (ytyp
t)+λrvar (∆rt)+λwvar (wt)
where var (.)is the variance operator, and 8k=fy,r,wg,λk
represents the weight on the respective variance.
Iπtis price-in‡ation, ytyp
tthe output-gap, ∆rtnominal
interest rate di¤erential, and wtwage-in‡ation.
16 / 27
1955-2017
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
0.3
0.4
2007-2017
1 2 3 4 5 6 7 8 9 1011 12
0
0.1
0.2
0.3
0.4
1985-2007
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
0.3
0.4
1955-1985
1 2 3 4 5 6 7 8 9 101112
0
0.1
0.2
0.3
0.4
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
1 2 3 4 5 6 7 8 9 1011 12
0
0.2
0.4
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
1 2 3 4 5 6 7 8 9 101112
0
0.05
0.1
0.15
1 2 3 4 5 6 7 8 9 1011 12
0
0.05
0.1
0.15
1 2 3 4 5 6 7 8 9 101112
0
0.05
0.1
0.15
1 2 3 4 5 6 7 8 9 101112
0
0.05
0.1
0.15
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 1011 12
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 101112
0
0.2
0.4
0.6
Estimated variances for each period and each rule.
1 2 3 4 5 6 7 8 9 10 11 12
25.1
34.1
43.0
27.8
36.7
45.6
30.5
39.4
48.3
37.1
46.0
54.9
39.8
48.7
57.6
42.5
51.4
60.3
49.1
58.0
66.9
51.7
60.6
69.5
54.4
63.3
72.2
24.1
28.4
32.7
27.4
31.7
36.0
30.7
35.0
39.3
65.2
68.5
71.8
94.2
98.2
34.8
43.0
38.3
46.4
41.7
49.9
71.1
74.5
78.0
74.8
62.7
77.8
50.5
65.6
80.7
60.8
76.0
91.1
63.8
78.9
94.0
66.7
81.9
97.0
74.6
62.5
77.5
50.5
65.5
80.5
60.7
75.7
90.7
63.6
78.6
93.6
66.6
81.5
96.5
15.6
22.1
28.5
19.0
25.4
31.8
22.3
28.7
35.2
38.2
44.6
51.1
41.5
48.0
54.4
44.8
51.3
57.7
60.7
67.2
73.6
64.1
70.5
77.0
67.4
73.8
80.3
25.3
31.3
37.3
29.4
35.4
41.4
39.5
45.5
42.8
48.9
54.9
46.9
53.0
59.0
51.0
57.0
63.1
60.4
66.4
72.5
64.5
70.5
76.5
68.6
74.6
80.6
16.6
26.1
35.5
20.8
30.2
39.6
24.9
34.3
43.7
31.1
40.5
49.9
35.2
44.6
54.0
39.3
48.7
58.1
45.5
54.9
64.3
49.6
59.0
68.5
53.7
63.2
72.6
16.5
35.4
54.3
20.7
39.6
58.5
24.9
43.8
62.7
35.6
54.5
73.4
39.8
58.7
77.6
44.0
62.9
81.8
54.7
73.6
92.5
58.9
77.8
96.7
63.1
82.0
100.9
56.6
60.9
59.9
64.2
63.2
67.5
89.0
93.3
97.6
92.3
96.6
100.9
95.6
99.9
104.2
36.4
49.4
62.4
40.4
53.4
66.4
44.4
57.4
70.4
52.3
65.3
78.3
56.3
69.3
82.3
60.3
73.3
86.3
68.2
81.2
72.3
85.2
76.3
89.3
102.3
26.7
30.1
33.5
54.8
62.9
58.2
66.4
61.6
69.8
82.8
91.0
99.2
86.3
94.4
102.6
89.7
97.9
106.0
28.3
43.5
58.6
31.3
46.4
61.5
34.2
49.4
64.5
44.6
59.7
47.5
28.6
43.6
58.5
31.5
46.5
61.5
34.4
49.4
64.4
44.6
59.6
47.6
28.1
47.9
67.8
31.1
50.9
70.8
34.1
54.0
73.8
48.6
68.5
88.4
51.7
71.5
91.4
54.7
74.6
94.4
69.2
89.1
108.9
72.3
92.1
112.0
75.3
95.1
115.0
31.0
57.2
83.4
34.5
60.7
86.9
38.1
64.3
90.5
51.6
77.7
103.9
55.1
81.3
107.5
58.7
84.8
111.0
72.1
98.3
124.5
75.7
101.9
128.1
79.2
105.4
131.6
33.4
CB losses, for each rule, between 1955 and 2017. T he shading schem e is de…ned
separately in relation to each line. The lighter the shading is, the sm aller the loss.
1 2 3 4 5 6 7 8 9 10 11 12
3.9
6.1
8.2
4.7
6.8
9.0
5.5
7.6
9.8
4.9
7.1
9.2
5.7
7.9
10.0
6.5
8.6
10.8
5.9
8.1
10.2
6.7
8.9
11.0
7.5
9.7
11.8
3.9
5.9
7.9
4.8
6.8
8.8
5.7
7.7
9.7
4.8
6.8
8.9
5.7
7.7
9.7
6.6
8.6
10.6
5.7
7.7
9.8
6.6
8.6
10.7
7.5
9.5
11.5
4.1
7.6
11.1
5.1
8.6
12.1
6.2
9.7
13.2
6.4
9.9
13.4
7.5
11.0
14.5
8.5
12.0
15.5
8.8
12.3
15.8
9.8
13.3
16.8
10.8
14.3
17.8
4.5
7.5
10.5
5.4
8.4
11.4
6.3
9.3
12.3
5.6
8.6
11.6
6.6
9.6
12.5
7.5
10.5
13.5
6.8
9.8
12.8
7.7
10.7
13.7
8.6
11.6
14.6
15.9
16.8
13.3
17.7
13.6
17.9
14.5
18.8
15.4
19.7
18.3
19.2
20.1
9.0
12.5
9.6
13.1
10.3
13.8
11.3
14.8
11.9
15.4
12.6
16.1
13.6
17.1
14.3
17.8
14.9
18.4
3.9
5.8
7.6
4.7
6.5
8.4
5.5
7.3
9.2
4.7
6.6
8.5
5.5
7.4
9.3
6.3
8.2
10.0
5.6
7.5
9.3
6.4
8.2
10.1
7.1
9.0
10.9
3.8
5.7
7.5
4.6
6.5
8.3
5.5
7.3
9.1
4.7
6.5
8.4
5.5
7.3
9.2
6.3
8.1
10.0
5.5
7.3
9.2
6.3
8.2
10.0
7.1
9.0
10.8
4.4
7.6
10.7
5.4
8.6
11.8
6.4
9.6
12.8
6.1
9.3
12.5
7.1
10.3
13.5
8.1
11.3
14.5
7.9
11.0
14.2
8.9
12.0
15.2
9.9
13.1
16.2
3.8
6.4
9.0
4.5
7.1
9.7
5.3
7.9
10.5
4.4
7.0
9.6
5.2
7.8
10.4
6.0
8.6
11.2
5.1
7.7
10.3
5.9
8.5
11.1
6.7
9.3
11.9
5.1
9.5
13.8
6.0
10.4
14.8
6.9
11.3
15.7
7.2
11.5
8.1
12.4
9.0
9.2
10.1
11.0
5.7
10.0
14.3
6.6
10.9
15.2
7.5
11.8
16.1
7.7
12.0
16.3
8.6
12.9
17.2
9.5
13.8
18.1
9.7
14.0
10.6
14.9
11.5
15.8
5.5
6.1
6.8
7.8
8.5
9.1
10.1
10.8
11.4
5.3
12.5
19.7
6.4
13.6
20.8
7.5
14.7
22.0
9.1
16.4
23.6
10.3
17.5
24.7
11.4
18.6
25.8
13.0
20.2
27.4
14.1
21.3
28.5
15.2
22.4
29.6
CB losses, for each rule, between 2007 and 2017. T he shading schem e is de…ned
separately in relation to each line. The lighter the shading is, the sm aller the loss.
1 2 3 4 5 6 7 8 9 10 11 12
4.2
6.2
8.2
4.8
6.8
8.8
5.4
7.4
9.5
8.8
10.8
12.8
9.4
11.4
13.5
10.0
12.0
14.1
13.4
15.4
17.4
14.0
16.0
18.1
14.6
16.7
18.7
5.2
6.6
8.0
5.9
7.3
8.7
6.6
8.0
9.4
8.5
9.9
11.3
9.3
10.7
12.1
10.0
11.4
12.8
11.9
13.3
14.7
12.6
14.0
15.4
13.3
14.7
16.1
7.3
9.2
8.2
10.0
9.0
10.8
9.4
11.2
13.0
10.2
12.1
13.9
11.1
12.9
14.7
13.3
15.1
16.9
14.1
15.9
17.8
15.0
16.8
18.6
10.5
14.0
17.5
11.2
14.7
18.2
12.0
15.5
19.0
14.4
17.9
21.4
15.1
18.6
22.1
15.9
19.4
22.9
13.5
5.0
6.4
7.8
5.7
7.1
8.5
6.4
7.8
9.2
9.7
11.1
12.4
10.4
11.8
13.2
11.1
12.5
13.9
14.3
15.7
17.1
15.1
16.4
17.8
15.8
17.2
18.5
4.7
6.1
7.4
5.5
6.8
8.2
6.2
7.5
8.9
9.5
10.9
12.2
10.2
11.6
13.0
11.0
12.3
13.7
14.3
15.7
17.0
15.0
16.4
17.8
15.8
17.1
18.5
5.0
6.6
8.1
5.8
7.4
9.0
6.6
8.2
9.8
9.7
11.3
12.9
10.6
12.1
13.7
11.4
12.9
14.5
14.5
16.1
17.6
15.3
16.9
18.4
16.1
17.7
19.2
4.3
8.2
5.1
8.9
12.7
5.8
9.6
13.4
10.4
14.2
18.1
11.1
14.9
18.8
11.8
15.7
19.5
16.5
20.3
17.2
21.0
24.8
17.9
21.7
25.6
5.5
6.3
7.2
6.6
10.1
13.6
7.3
10.8
14.3
8.1
11.6
15.1
5.8
9.1
12.5
6.5
9.8
13.2
7.1
10.5
13.8
12.1
15.5
18.8
12.8
16.1
19.5
13.4
16.8
20.2
18.4
21.8
25.1
19.1
22.4
25.8
19.8
23.1
26.5
6.0
9.5
13.1
6.7
10.2
13.7
7.3
10.9
14.4
13.9
17.4
21.0
14.6
18.1
21.6
15.2
18.8
22.3
21.8
25.3
28.9
22.5
26.0
29.5
23.2
26.7
30.2
6.5
9.4
12.3
7.1
10.0
12.9
7.7
10.6
14.2
17.1
19.9
14.7
17.6
20.5
15.3
18.2
21.1
21.8
24.7
27.6
22.4
25.3
28.1
22.9
25.8
28.7
5.5
11.0
16.5
6.5
12.0
17.5
7.5
13.0
18.5
14.1
19.5
25.0
15.0
20.5
26.0
16.0
21.5
27.0
22.6
28.1
33.5
23.6
29.0
34.5
24.6
30.0
35.5
12.0
24.1
CB losses, for each rule, between 1985 and 2007. T he shading schem e is de…ned
separately in relation to each line. The lighter the shading is, the sm aller the loss.
1 2 3 4 5 6 7 8 9 10 11 12
34.2
38.0
41.9
39.4
43.3
47.1
44.7
48.6
52.4
55.2
52.8
56.6
60.5
58.0
61.9
65.7
60.8
64.7
68.5
66.1
69.9
73.8
71.4
75.2
79.0
41.4
44.8
47.3
50.8
53.3
56.7
56.2
61.1
66.0
64.1
69.0
73.9
72.1
77.0
81.9
60.1
66.1
72.2
60.3
66.3
72.3
58.3
64.0
69.7
45.3
52.9
51.0
62.6
58.6
70.3
66.3
77.9
25.8
28.1
30.4
32.4
34.7
37.0
38.9
41.3
43.6
36.1
38.4
40.7
42.6
45.0
47.3
49.2
51.5
53.8
46.3
48.7
51.0
52.9
55.2
57.5
59.5
61.8
64.1
47.3
53.5
59.6
65.1
68.8
67.6
71.3
75.0
73.7
77.4
81.1
46.4
53.0
48.3
60.1
55.0
66.8
61.7
73.5
47.5
51.3
37.9
43.9
49.8
52.2
55.6
59.1
58.1
61.6
65.0
64.1
67.5
70.9
66.4
69.9
73.3
72.4
75.8
79.2
78.3
81.7
85.2
43.2
48.1
53.0
51.1
56.0
60.9
59.1
64.0
68.9
49.7
54.6
59.5
57.6
62.5
67.4
65.6
70.5
75.4
38.9
44.5
50.1
45.2
50.8
56.4
51.5
57.1
62.7
57.5
63.1
68.7
63.7
69.3
74.9
70.0
75.6
81.2
76.0
81.6
87.2
82.3
87.9
93.5
88.6
94.2
99.8
42.6
51.8
61.1
48.7
57.9
67.1
54.7
63.9
73.1
51.4
60.6
69.8
57.4
66.6
75.8
63.4
72.7
81.9
69.3
78.5
75.4
84.6
81.4
90.6
42.2
51.7
61.2
48.2
57.7
67.2
54.2
63.7
73.2
51.2
60.7
70.2
57.2
66.7
76.2
63.3
72.8
82.3
69.8
79.3
75.8
85.3
81.8
91.3
41.2
53.2
65.1
46.9
58.9
70.8
52.6
64.6
76.5
49.7
61.7
73.6
55.5
67.4
79.3
61.2
73.1
85.1
70.2
82.2
75.9
87.9
81.7
93.6
39.6
51.2
62.8
47.2
58.9
70.5
54.9
66.5
78.1
56.9
68.5
64.6
76.2
60.6
72.2
83.8
74.2
81.9
89.5
45.3
47.8
50.2
52.1
54.6
57.1
59.0
61.4
63.9
56.5
59.0
61.5
63.4
65.8
68.3
70.2
72.7
75.1
67.7
70.2
72.7
74.6
77.1
79.5
81.4
83.9
86.4
39.9
43.6
46.1
49.8
52.2
55.9
50.7
54.4
58.1
56.8
60.5
64.2
63.0
66.7
70.4
61.4
44.4
56.2
68.0
51.1
62.9
74.7
57.7
69.5
81.3
58.2
70.0
64.8
76.6
59.7
71.5
83.3
71.9
78.6
85.3
CB losses, for each rule, between 1955 and 1985. T he shading schem e is de…ned
separately in relation to each line. The lighter the shading is, the sm aller the loss.
Intro ducti on
Mod els
Resul ts
Conc lusion
Parame ters and …tting
Asses sment
Current loss functions
IRanking of rules:
IFollows values of L function given by each line.
IChanges with weighting scheme (from CB’s preferences).
IDuring GFC/ZLB Fed would have minimized losses via NGDP
rules in level but di¤erence of loss minimal with some Taylor
type rules.
23 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Summary
1955-2017 2007-2017 1985-2007 1955-1985
Fitting
Marginal density 5 12 12 1
Central bank loss
Current 9,11 9,10 (1,2,12) 2,10 (1,9) 10
Forecasted 9,12 9,12 (10) 10 (11) 10 (12)
Table: Summary of the best rule(s) for each criterion. Rules close to the
best one(s) are in parentheses.
IFitting:
Ia di¤erent rule for each period, but 12 twice.
IFed may have changed strategy during GM.
ILosses:
Isome NGDP in level rules best most of the time (some Taylor
type close) but not one that dominates whatever the period. 25 / 2 7
Intro ducti on
Mod els
Resul ts
Conc lusion
Policy implications
IIrrespective of the period in question, central bank’s objectives
are not achieved by one single rule.
IFor each type of period (more or less stable, crisis, recovery), a
given central bank reaction function performs better than
others.
IParameter estimates change with period for any monetary rule.
IYet current and forecasted losses indicate superiority of NGDP
rules in level except during the GM where the Taylor rule is
better with current losses (but NGDP in level is close).
IIn …ne:
INGDP in level rules most frequently indicated, especially
during crisis.
IBut some Taylor type rules also perform well, especially during
more stable periods.
INecessary to regularly re-estimate the models, thus the
parameters, to better …t the dynamics of the economy.
26 / 27
Intro ducti on
Mod els
Resul ts
Conc lusion
Conclusion
ICBs’objectives not achieved by one single empirical rule with
same weight to each variable entering the rule. For each type
of period (more or less stable, crisis, recovery) a speci…c
reaction function performs better than others.
ICBs which base their forecast and policy on such models and
rules should refresh their estimates regularly.
IPolicy makers should estimate CB losses (current or
forecasted) via several empirical monetary rules and models to
better assess their interest rate decisions.
27 / 27
