Producing forecasts with DSGE models by gdc15591

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									 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,
  e.g. relative price of tradables / non-tradables
          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
• Tradables and non-tradables driven by distinct
  unit-root productivity processes (not
  cointegrated)
• Utility with consumption of tradables and non-
  tradables
             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
            2. Adding judgment:
                   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
  – have access to off-model information
• 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
                 2. Adding judgment:
                     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
                 2. Adding judgment:
                        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
                2. Adding judgment:
                       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 instead
• Forward expansions lead to Beveridge-Nelson
  decomposition
   3. Communicating forecasts:
   Example of reconciliation tree
            Policy rate


            Headline        Policy
            inflation     smoothing


              Non-        Residential
Tradables                               Petrol
            tradables     construct’n


              RMC         Persistence



             Output       Real wages             Real rate


             Relative        Total
                                                 Wealth
              price       consumpt’n
              3. Communicating forecasts:
           Example of one reconciliation node
                                 RMC in non-tradables
 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
  adjusted for deterministic drift
   ~ = 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...)

								
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