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					Estimation, Calibration, and
  Validation of Structural
    Simulation Models

      Sherman Robinson
            IFPRI
          July 2002
                 Papers
• C. Arndt, S. Robinson, and F. Tarp (2002).
  “Parameter estimation for a computable
  general equilibrium model: a maximum
  entropy approch.” Economic Modeling, Vol
  19.
• S. Robinson, A. Cattaneo, and M. El-Said
  (2000). “Updating and Estimating a Social
  Accounting Matrix Using Cross Entropy
  Methods.” Economic Systems Research, Vol.
  13, No. 1.
                                               2
                Papers
• S. Devarajan and S. Robinson (2002).
  “The Impact of Computable General
  Equilibrium Models on Policy.”
  Presented at a conference on “Frontiers
  of Applied General Equilibrium
  Modeling” at Yale University, April 5-6,
  2002.

                                         3
                 Outline
• Model motivation and Design
  – Policy focus
  – Domain of applicability
• Model use
  – Static/dynamic
  – Dated/timeless
• Estimation, calibration, and validation
  – Maximum entropy econometrics
                                            4
    Desiderata for Policy Models
• Relevance
    – Link policy variables to outcomes
•   Transparency
•   Timeliness
•   Validation and estimation
•   Diversity of approaches

                                          5
     Domain of Applicability
• The domain of exogenous and
  endogenous variables for which the
  model is “valid.”
• Defined by choices in model design.
  – “Stylized” models
  – “Applied” models



                                        6
  Structural versus Reduced
         Form Models
• Desiderata argue for structural models
• Linking policy variables to outcomes
  – Aggregate and structural indicators:
    identifying winners and losers
• Transparency
  – “Black-box” syndrome


                                           7
              Model Use
• Static versus Dynamic
  – Comparative static
  – Recursive versus forward-looking dynamic
• Timeless versus dated
  – Timeless: counterfactuals not intended to
    match actual data
  – Dated: projections that can be compared
    with actual data
                                                8
      Timeless Static Mode
• Standard usage: comparative static
  – Change a few exogenous variables and
    compare results to base solution.
• Counterfactual question
  – What would the economy have looked like
    in the base year given the particular
    shocks under consideration?


                                              9
        Dated Static Mode
• Solve model for a second year some
  periods away from base year
  – Comparative static
• Incorporate actual or forecast changes
  in many exogenous variables and
  parameters
  – Historical or forward projection
  – Results are identified with particular year

                                                  10
   Timeless Dynamic Mode
• Steady-state equilibrium growth models
  – Shock model and compare new steady-
    state path with initial steade-state path
  – Analogous to timeless static: Do not
    associate time path with historical time
• Examples
  – Rational expectations dynamic CGE
    models
  – Real business cycle models
                                                11
      Dated Dynamic Mode
• Projection models
  – Recursive dynamic
  – Forward-looking dynamic
• Results can be tested agains historical
  data
  – Similar to dynamic macro-econometric
    models

                                            12
               Validation
• Validation by comparing explicit results
  with historical data can only be done for
  dated models
• Timeless models must be validated
  heuristically
  – “Rough” comparision with historic episodes
  – “Reasonableness” of specification and
    parameters
                                             13
      Parameter Estimation
• Two kinds of parameters
  – Share parameters: cost shares,
    expenditure shares, savings rates, tax
    rates, import and export shares
  – Elasticity parameters: describe the
    curvature of various structural functions
    (e.g., production, utility, import demand,
    export supply)

                                                 14
      Parameter Estimation
• Share parameters can be estimated
  from a based SAM
  – Benchmark calibration: base data are
    assumed to be a solution of the model
• Estimating elasticities requires
  additional information
• Validation requires “good” estimation

                                            15
   Estimation and Validation
• In standard econometric practice, model
  estimation and validation are done
  together.
  – Estimate parameters so that model tracks
    historical data as closely as possible
• Issue of domain of applicability
  – Historical data must include information
    relevant for shocks to be analyzed
                                               16
          Estimation: SAM
• SAM estimation
  – Share parameters
  – Timeliness
  – Accounts define model structure
• Historical data versus “average” SAM
  for parameter estimation
  – Issue of agriculture: “typical” year

                                           17
      Estimation/Calibration
• Kehoe et al.: Spanish economy
• Gehlhar: backcasting with GTAP model
• Dixon et al.: two-period calibration with
  Orani model
• Dervis, de Melo, and Robinson: Turkish
  structural adjustment model


                                          18
      Validation: Questions
• Can the model track historical flows?
• Which parameter values enable the
  model to track historical flows best?
  – Trade parameters (import demand and
    export supply)
  – Production functions
  – Demand system

                                          19
              CGE Model

• A CGE model: F(X,Z,B) = 0 where:
  – F is a vector valued function
  – X is a vector of endogenous variables
  – Z is a vector of exogenous variables
  – B is a vector of behavioral parameters
  – number of equations = number of
    unknowns.

                                             20
Standard Econometrics
Linear model
Y  X  e
Estimate of  is given by :
ˆ  XX 1 X Y


                              21
     Standard Environment
• Lots of data relative to number of
  parameters being estimated.
• Strong assumptions about distribution of
  errors.
  – Normal, mean of zero, single unknown
    parameter (variance).
• Assume no knowledge of parameter
  values. This is a moral imperative.

                                           22
        Standard Estimation
• Estimation criterion is to maximize
  within-sample “prediction” of various
  variables (Y).
• For efficient estimation, it is sufficient to
  represent the data by moments:
  – X′X and X′Y.
• Moments summarize all information
  needed for estimation.
                                              23
Information Theory Approach
• Goal is to recover parameters that
  generated the data we observe. Focus
  is on parameter estimation rather than
  prediction.
• Assume very little information about the
  error generating process and nothing
  about the functional form of the error
  distribution.
                                         24
       Estimation Principle

• Use all the information you have.
• Do not use or assume any information
  you do not have.
• Zellner: estimation using an efficient
  “information processing rule”.



                                           25
  Cross-Entropy Estimation
View the model in the following form:
  – F’(Xt , Zt , B) = 0
  – where t is a time subscript and
  – Yt= G(Xt , Zt , B) = et
  – where G(X0 , Z0 , B) = e0 = 0,
  – Yt is a vector of historical targets, and
  – G(.) calculates target values from
    model results.

                                                26
    Cross-Entropy Estimation
• Impose most elements of Zt.
• Choose B (and some elements of Zt,
  particularly technical change) such that:
  – 1) The errors are small and
  – 2) We are entropy close to our prior values on the
    elements of B.


• Choose the relative importance of the errors
  and our prior values.
                                                     27
   Trade-off Between Error
    and Parameter Priors
• GDPt actual = GDP tpredicted + et
• B must fall within some (reasonable)
  bound with a priordistribution:
  – Blow <= B <= Bhigh
• The maximum entropy procedure
  attempts to choose errors close to zero
  and parameters, B, close to center of the
  prior distributions.
• Can choose the relative weights of the
  two criteria.
                                              28
    CGE Model Estimation


      F(X, Z, , )  0
          ( Z t ' , ).
F(X t , Z , Z , , )  0  t  T
       o
       t
           u
           t


                               29
 CGE Model Estimation

Yt  G(X t , Z , Z , , )  e t
                    o
                    t
                        u
                        t
       M
 k   p km v km
      m 1

       J
etn   rtnj wtnj
       j 1

                                   30
                  CGE Model Estimation
                   K   M
                                p km         T    N    J    rtnj 
Min            1   p km Log 
                               q       2    rtnj Log 
                                                             s 
                                                                    
                                km 
   u
p ,r , Zt         k 1 m 1                   t 1 n 1 j 1  tnj 

                                      
             F X t , Z , Z , B,   O t  T
                           o
                           t
                               u
                               t


                                           
            Yt  G X t , Z , Z , B,   e t t  T
                                   o
                                   t
                                       u
                                       t


                         PZT , B
                                                                31
CGE Model Estimation
              J
e tn   rtnjw tnj t  T, n  N
              j1

               M
B k   p km v km k  K
              m 1
 J

r
 j 1
        tnj     1 t  T , n  N .

M
 p km  1 k  K
m 1
                                      32
    Application to Mozambique
•   Single country CGE model
•   Six commodities and a commerce activity
•   Two households: rural and urban
•   Rural and urban labor types
•   Cobb-Douglas technology
•   LES demand system
•   Home consumption
•   Armington import functions
•   CET function on exports
                                              37
 Estimated Parameter Values
• Armington import elasticities by commodity.
• CET export elasticities by commodity.
• LES parameters by commodity and
  household.
• Technical change parameters by activity.
• Implicit subsidies to state owned enterprises
  during the period 1992-94.


                                                  38
               Conclusion
• ME/CE estimation supports use of
  information in many forms and from
  many sources in estimating structural
  parameters
  – Very powerful and flexible approach
  – Particularly well suited for estimation of
    structural models


                                                 39
            Conclusion
• Productive tension between policy
  applications and developments in
  theory, econometrics, and data.
• Advances in software, econometrics,
  and theory are narrowing the gaps and
  supporting productive collaboration
  between theorists, applied
  econometricians, and policy modelers.
                                          40

				
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posted:5/6/2010
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