Modeling Consumer Decision Making and Discrete Choice Behavior

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Econometrics in Health Economics Discrete
Choice ModelingandFrontier Modeling and
Efficiency EstimationProfessor William
GreeneStern School of BusinessNew York
UniversitySeptember 2-4, 2007
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Application to Spanish Dairy Farms
N 247 farms, T 6 years (1993-1998)
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Using Farm Means of the Data
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OLS vs. Frontier/MLE
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JLMS Inefficiency Estimator

• FRONTIER LHS the variable
• RHS ONE, the
  variables
• EFF the new variable
  
• Creates a new variable in the data set.
• FRONTIER LHS YIT RHS X
• EFF U_i

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Half Normal vs. Exponential
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Ranking Observations

• CREATE newname Rnk ( Variable )
• Creates the set of ranks. Use in any
  subsequent analysis.

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Confidence Intervals for Technical
Inefficiency, u(i)
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Confidence Intervals for Technical
Efficiency, Exp-u(i)
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The Cost Frontier Model
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The Linear Homogeneity Restriction
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Translog vs. Cobb Douglas
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Cost Frontier Command

• FRONTIER COST
• LHS the variable
• RHS ONE, the
  variables
• EFF the new variable
  
• e(i) v(i) u(i) u(i) is still positive

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Estimated Cost Frontier
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JLMS Inefficiency Estimator

• FRONTIER COST LHS the variable
• RHS ONE, the
  variables
• EFF the new variable
  
• Creates a new variable in the data set.
• FRONTIER COST
• LHS YIT RHS X
• EFF U_i

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Cost Frontier Inefficiencies
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Normal-Truncated NormalFrontier Command

• FRONTIER COST
• LHS the variable
• RHS ONE, the
  variables
• Model Truncation
• EFF the new variable
  
• e(i) v(i) /- u(i)
• u(i) U(i), U(i) Nµ,?2
• The half normal model has µ 0.

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Truncated Normal Model
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Half Normal
Truncated Normal
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Multiple Output Cost Function
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Observations

• Truncation Model estimation is often unstable
• Often estimation is not possible
• When possible, estimates are often wild
• Estimates of u(i) are usually only moderately
  affected
• Estimates of u(i) are fairly stable across models
  (exponential, truncation, etc.)

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Assignment

• Christensen/Greene Electricity Application
  Production vs. Cost frontier
• Airlines Data Frontier Model Building
• Banking Data Multiple Output Cost Function

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WHO Data
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Heterogeneous Frontier Command

• FRONTIER COST
• LHS the variable
• RHS ONE, the
  variables,
• the additional
  variables
• EFF the new variable
  
• e(i) v(i) /- u(i)

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Heterogeneous Frontier Model

• FRONTIER LHS LDALE
• RHS ONE,LHEXP,LHEXP2,LEDUC,
• VOICE,GEFF,LPOPDEN,TROPICS
• EFF UI_WHO

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Heteroscedasticity
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Model Command for Heteroscedasticity
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Heterogeneity in the Mean of u(i)
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Telling NLOGIT You are Fitting a Panel Data Model

• Balanced Panel
• Model PDS number of periods
• REGRESS Lhs Milk Rhs One,Labor Pds
  6 Panel
• (Note Panel is needed only for REGRESS)
• Unbalanced Panel
• Model PDS group size variable
• REGRESS Lhs Milk Rhs One,Labor
• Pds FarmPrds Panel
• FarmPrds gives the number of periods, in
  every period.

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Group Size Variables for Unbalanced Panels
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Creating a Group Size Variable

• Requires an ID variable (such as FARM)
• (1) Set the full sample exactly as desired
• (2) REGRESS LHSOne Rhs One Panel STR
  ID
• where ID is the identification variable,
  e.g., STRFARM
• This creates a new variable named _GROUPTI. Now
  use
• Pds _Groupti

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Application to Spanish Dairy Farms
N 247 farms, T 6 years (1993-1998)
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Exploring a Panel Data Set Dairy
REGRESS Lhs YIT RHS
COBBDGLS PANEL PDS 6
REGRESS Lhs YIT RHS
COBBDGLS PANEL PDS 6
Het Group
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Nonlinear Panel Data Models
MODEL NAME Lhs
RHS PDS the
specification any
other model parts ALL PANEL DATA MODEL
COMMANDS ARE THE SAME
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Panel Data Frontier Model Commands

• FRONTIER LHS COST
• RHS
• EFF
• PDS
• ... the rest of the model
• any other options

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Pitt and Lee Random Effects

• FRONTIER LHS COST
• RHS
• EFF
• PDS
• any other options
• This is the default panel model.

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Pitt and Lee Random Effectswith
Heteroscedasticity Time Invariant Inefficiency

• FRONTIER LHS COST
• RHS
• EFF
• PDS
• HET HFU
• HFV

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Pitt and Lee Random Effectswith
Heteroscedasticity and Truncation Time Invariant
Inefficiency

• FRONTIER LHS COST
• RHS
• EFF
• PDS
• HET HFU
• HFV
• MODEL T RH2 One,

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Pitt and Lee Random Effectswith
HeteroscedasticityTime Invariant Inefficiency

• FRONTIER LHS COST
• RHS
• EFF
• PDS
• HET HFU
• HFV

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Schmidt and Sickles Fixed Effects

• REGRESS LHS RHS
• PDS PANEL PAR FIXED
• CREATE AI ALPHAFE ( id )
• CALC MAXAI Max(AI)
• CREATE UI MAXAI AI
• (Use Minimum and AI - MINAI for cost.)

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True Random EffectsTime Varying Inefficiency

• FRONTIER LHS COST RHS
• FRONTIER LHS COST RHS
• PDS Halton (a good
  idea) PTS number
• RPM FCN ONE (n)
• EFF
• Note, first and second FRONTIER commands are
  identical. This
• sets up the starting values.

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True Fixed EffectsTime Varying Inefficiency

• FRONTIER LHS COST RHS
• FRONTIER LHS COST RHS
• PDS
• FEM
• EFF
• Note, first and second FRONTIER commands are
  identical. This
• sets up the starting values.

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Battese and CoelliTime Varying Inefficiency

• FRONTIER LHS COST RHS
• PDS
• MODEL BC
• EFF
• This is the default specification, u(i,t)
  exph(t-T) U(i)
• To use the extended specification,
  u(i,t)expdz(i) U(i)
• Het
• HFU variables

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Other Models

• There are many other panel models with time
  varying and time invariant inefficiency,
  heteroscedasticity, heterogeneity, etc.
• Latent class,
• Random parameters
• Sample selection,
• And so on.