Large Datasets, Small Models and
Monetary Policy in Europe∗
Carlo A. Favero
Massimiliano Marcellino
Bocconi University, IGIER and CEPR
Model Evaluation in Macroeconomics, Oslo May 2005
∗
We thank Jordi Galì, two referees, Luca Sala and participants in the CEPR-Bank
of Italy conference on ”Monitoring the euro area business cycle” for comments. Nicola
Zaniboni provided excellent research assistance. This paper is part of a research project
on ”Factor models and macroeconomic forecasting” financed by the Italian Ministry for
Research and Education (MURST).
1
Introduction
• Economic Policy decisions are based on very large information sets
• Small DSGE models are establishing themselves as the state of art tool
for analyzing policies.
• DSGE models are empirically evaluated using VARs:
Bo Yt = AEt (Yt+1 ) + B1 Yt−1 + F ut
X
S J Et ut+j
Yt = P Yt−1 + D
DSGE
V AR
D = (Bo − AP )−1 F
• How do we check for misspecification in our VAR ???
1
2
Factor models and the assessment of misspecification and omitted information
• use a large dataset Xt and model it as:
Xt = ΛFt + et ,
(1)
• Assess the effect of estimating Taylor rules by using factors as instruments for expected inflation and the output gap.
• Augment Structural VAR with factors and assess their impact on the
description of the effects of policy. How monetary policy shocks differ
in a FAVAR? How the effect of monetary policy shocks differ in a
FAVAR ?
2
3
Factors and the effects of monetary policy
in Europe
3.1
The data and the factors
The dataset we adopt comes from Marcellino, Stock and Watson (2000a,
2000b). It includes the OECD main economic indicators, monthly, for the
period 1982:1-1997:8, There are about 50 variables for each country, that usually contain, among others, industrial production and sales (disaggregated
by main sectors); new orders in the manufacturing sector; employment, unemployment, hours worked and unit labor costs; consumer, producer, and
wholesale prices (disaggregated by type of goods); several monetary aggregates (M1, M2, M3), savings and credit to the economy; short term and long
term interest rates, and a share price index; the effective exchange rate and
the exchange rate with the US dollar; several components of the balance of
payments; and other miscellanea variables. To model these variables we use
a factor model, whose standard formulation is
Xt = ΛFt + et ,
(2)
where Ft is a r × 1 vector of common factors, whose loadings are grouped in
the N × r matrix Λ, et is an N × 1 vector of idiosyncratic disturbances, N is
the number of variables under analysis, much larger than r, and t = 1, ..., T .
We consider two types of factors.
• The first one is obtained from a model where Xt includes all the variables in the dataset.
• The second one is specific for each country, i.e., Xt only includes the
variables of a specific country. Marcellino et al (2000b) refer to the
former as pooled factors and to the latter as country-specific factors.
3
3.2
Taylor rules
The estimated factors are particularly useful for forecasting inflation. Hence,
they can be exploited to produce the inflation forecasts that appear in a
forward looking Taylor rule.
The Taylor rule for Germany takes the form
rt = α + (1 − ρ)β(π t+12 − π ∗t ) + (1 − ρ)γ(yt − yt∗ ) + ρrt−1 + t ,
(3)
πet+12 is the forecast of the one year inflation rate made in period t, yt is real
output, and π ∗t and yt∗ are the desired levels of inflation and output. .
for France, Italy and Spain,
rit = (1 − ρ)rt + (1 − ρ)β(πit+12 − π ∗t ) + (1 − ρ)γ(yit − yit∗ ) + ρrit−1 +
it .
(4)
As a measure of π ∗t we use the official inflation target for Germany, while
the potential output yt∗ is the Hodrick Prescott (one-sided) filtered version
of the actual output series. For the interest rate, we use 3-month rates, in
particular the Fibor for Germany, the Pibor for France, and the interbank
rate for Italy and Spain.
We estimate the TR with and without factors.
4
To provide a further assessment of the role of factors we follow Bernanke
and Boivin (2000) and test for the significance in the Taylor rule of the fitted
values of the interest rate recursively regressed on the factors.
Hence, we estimate the equations
rt = α + (1 − ρ)β(b
π t+12 − π ∗t ) + (1 − ρ)γ(yt − yt∗ ) + ρrt−1 + ηb
rt + t ,
(5)
for Germany, and
π it+12 −π ∗t )+(1−ρ)γ(yit −yit∗ )+ρrit−1 +ηb
rt + it . (6)
rit = (1−ρ)rt +(1−ρ)β(b
where π
bt+12 is the estimated inflation from a regression of π t+12 on the in-
struments including the factors, while rbt is the estimated value from
rt = αFt−1 + ut ,
and test whether η = 0 using a robust t-test. Following Bernanke and Boivin
(2000), ηb
rt can be considered as an “excess policy response”.
5
3.3
Structural VARs
We estimate baseline VAR models for the European countries with a specification consistent with the forward-looking Taylor rules:
·
¸
·
¸ ·
¸
Xt
Xt−1
ut
A
= A (L)
+
,
it
it−1
um
t
(7)
where the vector Xt contains domestic output gap, domestic inflation, commodities price inflation, and the US Dollar-Deutschemark exchange rate in
the case of Germany, while for the other three European countries the US
Dollar-Deutschemark exchange rate is substituted with the exchange rate of
the local currency vis-a-vis the Deutschemark, and the German policy rates.
The domestic policy rate is it . We then consider an alternative scenario based
on the inclusion of the factors as exogenous regressors in the VAR.
• We evaluate the “economic” importance of the inclusion of factors in
the VAR by looking at the response of the output gap and inflation
to domestic monetary policy in the baseline and in the alternative scenario.
• Finally, an alternative tool for the evaluation of the effects of monetary
shocks on the economy is the dynamic simulation of the following model
for each of our four countries of interest:
·
¸
·
¸ ·
¸
Xt
Xt−1
ut
A
= A (L)
+
.
it
it−1
6
(8)
Table 1: Forward-looking Taylor rules for Europe
Germany
France
Italy
Spain
β(s.e.)
CGG
3.17 (1.409) 0.75 (0.143) 1.72 (0.073) 1.02 (0.139)
CS+PL 1.33 (0.171) 0.73 (0.127) 1.79 (0.066) 1.46 (0.080)
CS
3.04 (1.255) 0.76 (0.138) 1.78 (0.079) 1.46 (0.098)
PL
1.53 (0.240) 0.83 (0.133) 1.79 (0.075) 1.52 (0.082)
γ(s.e.)
CGG
4.43 (3.107) 1.55 (0.212) 1.57 (0.299) 1.40 (0.248)
CS+PL 1.56 (0.392) 1.35 (0.144) 1.68 (0.277) 1.44 (0.185)
CS
3.68 (2.313) 1.47 (0.176) 1.67 (0.346) 1.62 (0.217)
PL
1.74 (0.604) 1.39 (0.181) 1.76 (0.343) 0.30 (0.180)
ρ(s.e.)
CGG
0.99 (0.006) 0.96 (0.003) 0.97 (0.003) 0.97 (0.003)
CS+PL 0.98 (0.004) 0.96 (0.002) 0.98 (0.003) 0.97 (0.002)
CS
0.99 (0.005) 0.96 (0.003) 0.98 (0.003) 0.97 (0.003)
PL
0.99 (0.005) 0.96 (0.003) 0.98 (0.003) 0.96 (0.003)
R2
CGG
0.985
0.972
0.966
0.961
CS+PL 0.986
0.972
0.966
0.961
CS
0.986
0.972
0.966
0.961
PL
0.986
0.972
0.966
0.961
S.E. of Regression CGG
0.246
0.426
0.581
0.625
CS+PL 0.246
0.424
0.582
0.630
CS
0.244
0.425
0.583
0.630
PL
0.245
0.425
0.583
0.637
J-Stat (Prob)
CGG
14.18 (0.99) 14.5 (0.99) 14.26 (0.99) 14.24 (0.99)
CS+PL 15.33 (0.99) 14.99 (0.99) 14.57 (0.99) 14.54 (0.99)
CS
15.11 (0.99) 14.78 (0.99) 14.43 (0.99) 14.41 (0.99)
PL
15.12 (0.99) 14.78 (0.99) 14.47 (0.99) 14.37 (0.99)
Notes: the estimated equations are rt = α +(1 −ρ)β(π t+12 −π ∗t ) + (1 −ρ)γ(yt −
yt∗ ) + ρrt−1 +
t
for Germany and rit
ρ)γ(yit − yit∗ ) + ρrit−1 +
it
= (1 − ρ)rt + (1 − ρ)β(π it+12 − π ∗t ) + (1 −
for France, Italy and Spain. GMM estimation over 1983:1-
1997:8 (except for Spain: 1984:1-1997:8). CGG is the set of instruments used in Clarida,
Galì and Gertler (1998). In the other models, four sets of factors were used: country
specific factors (CS), factors extracted from the 4-country merged dataset (PL4), factors
extracted from the EMU pooled dataset (PL) and (CS+PL).
7
Table 2: ”Excess policy response” analysis
Germany
France
Italy
Spain
β
(s.e.)
0.43
(0.189)
1.10
(0.192)
1.44
(0.734)
-1.13
(2.102)
γ
ρ
(s.e.)
(s.e.)
0.14
0.89
(0.102) (0.037)
0.24
0.90
(0.341) (0.027)
0.36
0.95
(0.434) (0 .025)
1.23
0.96
(1.392) (0.039)
η
(s.e.)
0.78 *
(0.125)
0.18 *
(0.050)
0.08
(0.261)
0.65
(0.490)
R2
S.E. of Regr.
0.987
0.235
0.974
0.414
0.967
0.572
0.963
0.612
* Significant at the 1% level
Notes: the estimated equations are rt
yt∗ ) + ρrt−1 + ηb
rt +
t
= α +(1 −ρ)β(b
π t+12 −π ∗t ) + (1 −ρ)γ(yt −
for Germany and rit
(1−ρ)γ(yit −yit∗ )+ρrit−1 +ηb
rt +
it
= (1 − ρ)rt + (1 − ρ)β(b
π it+12 − π ∗t ) +
France, Italy and Spain (see text for details). The
parameters are estimated by OLS over 1983:1-1997:8 (except for Spain: 1984:1-1997:8).
The table entries are the coefficient estimates (robust standard errors in brackets), Rsquared, and standard error of the regression.
8
Table 3: Actual and simulated macroeconomic variables
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π∗t )2
Actual CGG CS+PL Factors CS Factors PL Factors
Germany
4.02
0.41
3.53
3.09
2.57
2.41
2.00
2.40
2.38
2.38
4.20
3.82
4.07
4.03
4.27
2.26
1.56
2.15
2.15
1.70
France
6.42
5.34
5.85
6.32
6.23
3.57
3.45
3.55
3.58
3.57
1.77
1.73
1.63
1.66
1.56
5.23
4.88
5.20
5.22
5.18
Italy
9.72
8.47
8.84
8.36
8.64
6.34
6.46
6.34
6.39
6.32
5.31
5.01
5.06
5.06
5.07
22.31 23.15
22.34
22.69
22.61
Spain
13.80 10.05
10.77
11.16
11.86
6.51
6.47
6.54
6.43
6.52
4.74
4.87
4.86
4.78
4.72
21.65 21.43
21.93
21.47
21.61
Rt is domestic policy rate, yt∗ is potential
Notes: sample period is 1984:1-1997:8.
output (computed as the Hodrick Prescott filtered version of actual output) and
official inflation target for Germany. [Domestic monetary shock set to zero]
9
π∗t is the
Table 4: Actual and simulated macroeconomic variables
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π ∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π ∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π ∗t )2
V ar(Rt )
E(π t )
E(yt − yt∗ )2
E(π t − π ∗t )2
Actual CGG CS+PL Factors CS Factors PL Factors
Germany
4.02
0.41
0.20
0.29
0.31
2.41
2.00
2.15
2.23
2.09
4.20
3.82
3.72
3.67
3.49
2.26
1.56
0.76
0.81
1.00
France
6.42
5.34
0.57
5.53
0.63
3.57
3.45
3.79
3.74
3.87
1.77
1.73
1.34
1.56
1.47
5.23
4.88
2.04
1.93
2.22
Italy
9.72
8.47
3.55
3.36
1.83
6.34
6.46
6.62
6.56
6.33
5.31
5.01
4.66
4.836
5.98
22.31 23.15
19.01
17.88
17.01
Spain
13.80 10.05
14.67
3.75
9.54
6.51
6.47
6.63
10.18
6.52
4.74
4.87
4.79
8.29
4.54
21.65 21.43
19.20
59.41
17.32
Notes: sample period is 1984:1-1997:8.
Rt is domestic policy rate, yt∗ is potential
output (computed as the Hodrick Prescott filtered version of actual output) and
official inflation target for Germany. [Factors are excluded in the simulations]
10
π∗t is the
Figure 1̇: Residuals from Taylor rules, VARs without factors and VARs
with factors
G ermany
F rance
1.2
3
0.8
2
0.4
1
0.0
0
-0.4
-1
-0.8
-2
-1.2
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
RESTAY_CGG
RESVAR_CGG
RESVAR_CSPL
Italy
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
1986
1988
1990
1992
1994
1996
1994
1996
Sp a in
4
1984
1990
RESTAY_CGG
RESVAR_CGG
RESVAR_CSPL
1992
1994
1996
1984
RESTAY_CGG
RESVAR_CGG
RESVAR_CSPL
1986
1988
1990
1992
RESTAY_CGG
RESVAR_CGG
RESVAR_CSPL
Notes: each graph reports three measures of monetary policy shocks - the residuals from the policy rate equations of the baseline VAR with the CGG set of variables (RESVAR_BL), from an alternative VAR with country-specific and pooled factors
(RESVAR_CSPL), and from the Taylor rule estimated with the CGG set of instruments
(RESTAY_CGG) (the residual series from Taylor rules across different models are almost
identical).
11
Figure 2: Responses to one S.D shock to domestic policy rate - Germany
Output gap
Var with factors
VAR without factors
.8
.8
.6
.6
.4
.4
.2
.2
.0
.0
-.2
-.2
-.4
Inflation rate
5
10
15
20
25
30
35
40
45
50
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
-.2
5
Policy rate
-.4
10
15
20
25
30
35
40
45
50
.6
.6
.5
.5
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
5
10
15
20
25
30
35
40
45
5
50
10
15
20
25
30
35
40
45
50
Notes: the graphs report point estimates and confidence intervals of the impulse responses in the baseline VAR with the CGG set of variables and in the alternative VAR
with country specific + pooled factors .
12
Figure 3: Responses to one S.D shock to domestic policy rate - France
Output gap
VAR without factors
VAR with factors
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
-.4
Inflation rate
5
10
15
20
25
30
35
40
45
50
.3
.3
.2
.2
.1
.1
.0
.0
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
-.1
-.1
5
Policy rate
5
10
15
20
25
30
35
40
45
50
.6
.6
.5
.5
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
Notes: the graphs report point estimates and confidence intervals of the
impulse responses in the baseline VAR with the CGG set of variables and in the alternative
VAR with country specific + pooled factors.
13
Figure 4: Responses to one S.D shock to domestic policy rate - Italy
Output gap
VAR without factors
VAR with factors
.6
.6
.4
.4
.2
.2
.0
.0
-.2
-.2
-.4
-.4
-.6
Inflation rate
5
10
15
20
25
30
35
40
45
-.6
50
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
Policy rate
5
10
15
20
25
30
35
40
45
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
-.3
50
.8
.8
.6
.6
.4
.4
.2
.2
.0
.0
-.2
-.2
-.4
-.4
5
10
15
20
25
30
35
40
45
50
Notes: the graphs report point estimates and confidence intervals of the impulse
responses in the baseline VAR with the CGG set of variables and in the alternative VAR
with country specific + pooled factors.
14
Figure 5: Responses to one S.D shock to domestic policy rate - Spain
Output gap
VAR without factors
VAR with factors
.6
.6
.4
.4
.2
.2
.0
.0
-.2
-.2
-.4
-.4
-.6
-.6
Inflation rate
5
10
15
20
25
30
35
40
45
50
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
Policy rate
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
-.3
1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0
-0.4
-0.4
-0.8
-0.8
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
Notes: the graphs report point estimates and confidence intervals of the impulse
responses in the baseline VAR with the CGG set of variables and in the alternative VAR
with country specific + pooled factors
15
Figure 6: An alternative evaluation of the effects of monetary shocks
Inf lation rates
Output gaps
8
Policy rates
7
10
6
4
9
5
8
Germany
4
0
-4
3
7
2
6
1
5
0
-8
4
-1
-12
-2
1984
1986
1988
1990
1992
1994
1996
3
2
3
1984
1986
1988
1990
1992
1994
1996
12
14
10
12
8
10
6
8
4
6
2
4
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1
France
0
-1
-2
-3
-4
-5
0
1984
1986
1988
1990
1992
1994
1996
2
1984
8
20
4
16
0
12
-4
8
-8
4
-12
0
1986
1988
1990
1992
1994
1996
20
18
Italy
16
14
12
10
1984
1986
1988
1990
1992
1994
1996
8
6
1984
6
14
4
12
1986
1988
1990
1992
1994
1996
24
20
10
2
16
Spain
8
0
6
-2
12
4
-4
2
-6
0
1984
1986
1988
1990
1992
1994
1996
8
4
1984
1986
1988
1990
1992
1994
1996
Notes: each graph reports the simulated paths from the baseline model (CGG - dotted
line) and from the alternative scenario with country-specific + pooled factors (dashed line),
alongwith the actual variables (solid line).
16
Figure 7: An evaluation of the relevance of factors
Output gaps
Inf lation rates
8
Policy rates
7
10
6
4
9
5
8
4
Germany
0
-4
3
7
2
6
1
5
0
-8
4
-1
-12
-2
1984
1986
1988
1990
1992
1994
1996
3
2
3
1984
1986
1988
1990
1992
1994
1996
12
14
10
12
8
10
6
8
4
6
2
4
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1
France
0
-1
-2
-3
-4
-5
0
1984
1986
1988
1990
1992
1994
1996
2
1984
8
20
4
16
0
12
-4
8
-8
4
1986
1988
1990
1992
1994
1996
20
18
Italy
16
14
12
10
-12
1986
1988
1990
1992
1994
1996
6
1984
1986
1988
1990
1992
1994
1996
6
14
28
4
12
24
10
2
Spain
8
0
1984
20
8
0
16
6
-2
12
4
-4
2
-6
0
1984
1986
1988
1990
1992
1994
1996
8
4
1984
1986
1988
1990
1992
1994
1996
Notes: each graph reports the simulated paths from the baseline model (CGG - dotted
line) and from the alternative scenario with country-specific + pooled factors (dashed
line), alongwith the actual variables (solid line), where the factors are excluded from the
simulated model.
17
Figure 8: The uncertainty on the effects of monetary shocks
Output gaps
Policy rates
Inf lation rates
12
12
8
20
15
8
4
10
4
Germany
0
5
-4
0
0
-8
-4
-12
-8
-16
1984
France
-5
1986
1988
1990
1992
1994
1996
6
12
4
10
2
8
0
6
-2
4
-4
2
-6
0
-8
-10
1984
1986
1988
1990
1992
1994
1996
1986
1988
1990
1992
1994
1996
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
12
8
4
0
-4
1984
1986
1988
1990
1992
1994
1996
12
20
24
8
16
20
12
16
8
12
4
8
-12
0
4
-16
-4
4
1986
16
-2
1984
1984
Italy
0
-4
-8
1984
1986
1988
1990
1992
1994
1996
8
0
1984
1986
1988
1990
1992
1994
1996
14
40
12
4
30
10
20
Spain
8
0
6
10
4
-4
0
2
-8
-10
0
1984
1986
1988
1990
1992
1994
1996
1984
1986
1988
1990
1992
1994
1996
Notes: each graph reports bounds for dynamically simulated variables in the baseline
model with the CGG set of variables (thin lines) and in the alternative model with country
specific + pooled factors (thick lines).
18
4
What have we learned?
The better way to summarize our results is probably a brief evaluation of
what we have learned from the empirical investigation. Our first evidence is
that forward-looking Taylor rules for European countries are systematically
more precisely estimated when factors are included in the instrument set.
This evidence can be interpreted as a clear signal of the fact that central
banks employ a much wider information set than that included in small
macroeconometric models to forecast inflation and set their policy rates.
Moreover, the information summarized by the factors could have a direct
effect on the policy decisions.
Two questions arise naturally at this point:
a) Does this really matter? Are the effects of the mis-specification generated by under-parameterization statistically significant and economically important?
b) How far do we go in simply augmenting the small structural models
with the information contained in the factors?
19