Producing forecasts with DSGE models by gdc15591

VIEWS: 0 PAGES: 23

• pg 1
```									 Producing forecasts
with DSGE models:
Issues and solutions
I        d l i

Jaromir Benes
Reserve Bank of New Zealand
R       B k fN Z l d
DSGE forecast production at RBNZ

Raw        Monitoring     External
Judgment     Main risks
database      quarters     projections

Model-
equivalent
variables

SA &                      Historical
smoothing                  simulations

MV        In-sample
In sample       1st pass      2nd pass   Alte nati e
Alternative
filter      database      forecasts     forecasts    scenarios

Understand    Understand    Understand   Understand
Judgment
init.cond.     1st pass     2nd pass    alternatives
Some of the issues (and solutions)

1. Treating stochastic trends

2. Adding judgment to DSGE forecasts

3. Communicating DSGE forecasts
1. Stochastic trends

yp     y gg           y
• Data typically suggest many more than one
common real trend
• How we treat stochastic trends determines how
we set up initial conditions for forecasts
• Some of them important for monetary policy,
1. Stochastict trends:
Two types of solutions

Outside                    Inside
build a stationary model   introduce a number of
i       in h    d l
unit roots i the model
pre-filter data
accordingly                use sector-specific
c.
productivities et c
choose univariate or
multivariate methods       Kalman filter with
diffuse initial condition
1. Stochastic trends:
Inside solution
p
• BGP models with multiple stochastic trends
• No need to stationarise model: first- order
accurate solution valid with unit roots retained
• Taylor (log-)expansion around a snapshot of
BGP at an arbitrary date; Taylor coefficients
independent of that date
• Preferable form
⎡ at ⎤ ⎡T       0⎤   ⎡at −1 ⎤
⎢ x f ⎥ = ⎢F         ⎢ x f ⎥ + R et        ⎡ I T1 ⎤
0⎥                    T := ⎢
⎣ t ⎦ ⎣          ⎦   ⎣ t −1 ⎦
⎣ 0 T2 ⎥
⎦
xtb = U at
1. Stochastic trends:
Preferences & technology
p
• Stochastic trends in relative prices and real
quantities
– sector-specific productivities
– sector-specific iceberg costs, etc.
• Nominal expenditure ratios must stable in the
l        (for the         i t      l ti to hold)
long run (f th approximate solution t h ld)
• Implications for elasticities of substitution:
i    i long run
– unitary in l
– reduced in short run by deep habit, adjustment costs,
etc.
1. Stochastic trends:
Example of utility function
y
unit-root productivity processes (not
cointegrated)
• Utility with consumption of tradables and non-
max E 0 ∑ β t (log Γt + )

(   τ     τ
Γt := Ct − χ Ct −1   ) (
ω
Ctn   −χ      )
n 1−ω
Ct −1
1. Stochastic trends:
Curse of dimensionality
y
• KITT has more than 20 observables, very few
combinations pass co-integration tests
• Demand for pre-filtering (MPC & governor):
previous model’s legacy
• No unique/universal trend-cycle decomposition
within DSGEs
• Pragmatic solution?
– include only some (=policy important) trends
– pre-filter remaining trends
filt    ith         i t     imposed
– use MV filters with some consistency i     d
1. Stochastic trends:
Designing MV filters
• MV filter with I(2) (HP-like) trends
• NIPA identities and other definitions
– e.g. long-run sustainability of current account
• Would be identical to univariate filters...
p    g      /j g
• ...unless we start imposing tunes/judgment:
Automatic                    Forecast-specific
e.g.
stabilising trends in e g           e.g.
tuning e g
• nominal ratios            • gaps in GDP components
g                           g
• growth and interest rates • growth rates in relative
prices
in pre-sample and post-
sample
1. Stochastic trends:
Example of MV filter
Nominal consumption/GDP                      NT inflation               World oil price/World PPI
80                                      6                               500

78                                      4                               400

76                                      2                               300

74                                       0                              200
1992 1996 2000 2004 2008                1992 1996 2000 2004 2008         1992 1996 2000 2004 2008
Consumption gap                          Export gap                        Output gap
5                                      5                                 5

0
0                                                                        0
-5

-5                                     -10                                -5
1992 1996 2000 2004 2008                1992 1996 2000 2004 2008          1992 1996 2000 2004 2008
BOP and investment income rate          Consumption/GDP deflator          Consumption deflator/CPI
10                                    -180                              -665

8
-185                              -670
6

4                                    -190                              -675
1992 1996 2000 2004 2008                1992 1996 2000 2004 2008          1992 1996 2000 2004 2008
Why?
p j
• Core (DSGE) projection models must have g   good
forecasting properties to inform policy decisions
• ...but staff & policymakers
– process information in many other different ways
• Baseline needs to be staff projection combining
many pieces of information rather than model
i l ti
simulation
• Governor signs the baseline and the forecasts
need to reflect his beliefs
What kind?
Structural judgment               Reduced-form judgment
Conditional on distribution of
C di i      l   di ib i      f    Conditional on di ib i
C di i      l  distributions of
f
particular structural shocks      particular endogenous variables

Unanticipated mode                Anticipated mode
Future judgment not foreseen      Future judgment foreseen

Hard   di i
H d conditions                    Density conditions
D   i      di i
Judgment imposed as a single      Judgment imposed as a
point                             distribution

Reduced-form judgment:

y
Exactly determined                Underdetermined
Number of judgment conditions =   Number of judgment conditions =
number of shocks backed out       number of shocks backed out
How?
• Structural & unanticipated: Rather trivial...
xt = T xt −1 + R et
p
• Structural & anticipated: Solution needs to be
expanded forward
xt = T xt −1 + R0 et + R1 E t [et +1 ] +   + Rk E t [et + k ]
• Reduced-form & unanticipated: Equivalent to
Kalman filter
xt = T xt −1 + R et
Ct xt = yt + ωt
How?
p
• Reduced-form & anticipated, p  point forecast:
Extension of Waggoner-Zha for RE and
uncertainty in initial conditions
xt = T xt −1 + R0 et + R1 E t [et +1 ] +   + Rk E t [et + k ]
Ct xt = yt + ωt
• Find likelihood-maximising paths for
′
z = [xt′−1 et′ et′+ k ωt′ ωt′+ k ]
• Solve
min z ′ Ω + z s.t. C x = y + ω ⇒ D z = d
• Exactly determined solution independent of Ω
3. Communicating forecasts

y     policymakers who are non-
• Unravel story for p    y
modellers but understand models
• Maximise structural interpretation
• Many possible perspectives, e.g.
– contributions of individual historical shocks from
Kalman filter
– effects of individual data outturns on differences
between this and last forecast rounds
• Here: focus on reconciliation trees

16
3. Communicating forecasts:
Reconciliation trees
q                g
• Create a tree of equations following a certain
logic, choose LHS variables
• Quantify first-order effects of RHS variables
• Do not use t+1 terms; expand expectations
• Forward expansions lead to Beveridge-Nelson
decomposition
3. Communicating forecasts:
Example of reconciliation tree
Policy rate

inflation     smoothing

Non-        Residential

RMC         Persistence

Output       Real wages             Real rate

Relative        Total
Wealth
price       consumpt’n
3. Communicating forecasts:
Example of one reconciliation node
5

0

5
-5
2005:1     2006:1     2007:1          2008:1            2009:1   2010:1   2011:1
Weighted contributions
5

0
Real Wage
-5                   Economic activity
2005:1     2006:1     2007:1          2008:1            2009:1   2010:1   2011:1
Productivity shocks
10

0

-10
2005:1     2006:1     2007:1          2008:1            2009:1   2010:1   2011:1
3. Communicating forecasts:
Beveridge Nelson
Beveridge-Nelson
• Asymptotic forecast of any (unit-root) variable
~ = E [x ] − (d − d )
xt   t t +∞    t +∞ t

• Extremely easy to evaluate for triangular forms
at1 = at1 + T1 (I − T2 ) at2
~                       −1
⎡ at1 ⎤ ⎡ I T1 ⎤ ⎡at1−1 ⎤
⎢ 2⎥ = ⎢       ⎥⎢ 2 ⎥+      ~b = U a 1~
⎣at ⎦ ⎣0 T2 ⎦ ⎣at −1 ⎦
−1     xt      1   t

y
• Easy to evaluate contributions of individual
shocks and judgment
3. Communicating forecasts:
Beveridge Nelson
Example of Beveridge-Nelson
• Iterate UIP forward
[             (
st = E t st +∞ − ∑ it + k − it*+ k + )       ]
• Explain BN trends

[                   (
E t [st + ∞ ] = E t pt + ∞ − pt*+ ∞ − at + ∞ − at*+ ∞   )]
3. Communicating forecasts:
Beveridge Nelson
Example of Beveridge-Nelson
Nominal exchange rate and its Beveridge-Nelson
1.25

1.2

1 15
1.15

1.1

1.05

1

0.95

09
0.9

0.85
1994   1996   1998   2000   2002   2004   2006   2008   2010
Lessons learned from NZ experience

j                            p            g
• Projection models need to be exposed to a large
variety of (simple) techniques for modellers to:
– understand DSGE-based forecasts
– communicate the forecasts with non-modellers
– maximise the structural DSGE interpretation
Devices to translate model outcomes i
• D i              l      d l           into
language understandable to other staff and end-
users
• Everything needs to be applied effectively and
(that s
seamlessly (that’s what you get when using
IRIS...)

```
To top