Simultaneous Equations Models SEM Chapter 16

1
Simultaneous Equations Models (SEM) (Chapter 16)

• Course Applied Econometrics
• Lecturer Zhigang Li

2
Simultaneity

• Simultaneity is an important source of
  endogeneity
• Simultaneity arises when some explanatory
  variables are jointly determined with the
  dependent variable.
• These explanatory variables are generally
  endogenous.
• A Simultaneous Equation Model (SEM) explicitly
  models all those endogenous variables that are
  jointly determined.
• A correctly formed SEM is very useful because it
  could suggest instrumental variables to solve the
  simultaneity problem.

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A Classical Example of SEM

• Supply and demand for some product
• Labor Supply
• hsa1wß1z1u1
• Higher wage w, higher supply of labor. This is a
  positive causal effect on employees.
• Labor Demand
• hda2wß2z2u2
• Higher wage w, lower demand for labor. This is a
  negative causal effect on employers.
• Wage w is endogenous in equilibrium. Both zs are
  exogenous.

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IV

• OLS regression of h on w can not identify either
  the causal effect on employees or the causal
  effect on employers.
• IV
• If z1 and z2 are not the same, then z1 can be the
  IV for w in the demand equation while z2 can be
  the IV for w in the supply equation
• 2SLS can be used to estimate the coefficients of
  w in demand and supply equations separately.
• In general, you need at least as many IVs as
  endogenous variables for the IV method to work.

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Two More SEM ExamplesOne Good, One Bad (p.
528-29)

• Murder Rates and Police Force
• Reactions of potential murderers
• murdpc a1polpcß10ß11incomeu1
• Decision of city officials
• polpc a2murdpcß20u2
• Can we identify the effect of police force on
  murderers using IV approach?
• Housing Expenditures and Saving
• housing a1savingß10ß11incomeu1
• saving a2housingß20ß21incomeu2

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The Effect of an Open-Market Operation on Federal
Funds Rate (Hamilton, 1997)

• Bank reserves and federal funds rate are
  simultaneously determined.
• Liquidity Effect The effects on banks
• The Fed also chooses the supply of reserves each
  day based on the expected fed fund rate
• The study suggests using errors the Fed makes in
  forecasting the Treasury balance as an
  instrument.
• The errors induces changes in bank reserves but
  is exogenous to federal fund rates.
• The errors are not made public. The author
  construct a model to forecast the Treasury
  balance and used the fitted residuals as a proxy.

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Findings

• A reduction in nonborrowed researves of 30
  million may cause the federal funds rate to rise
  by 10 basis points.

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Does Trade Liberalization Harm the Environment?
(Dean, 2002)

• Effect on Firms
• ?Y aD?D aF?Fß(T)?d
• Effect on environment
• ?D ß(?p1-?p2-?T) aF?F
• Only Y and D are endogenous
• Using provincial data on Chinese water pollution,
  the study finds that income growth had
  significantly negative effect on pollution while
  the inverse effect is negligible.

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Effect of Pollution Control on Pollution (Wang
and Wheeler, 2005)

• Levy Equation
• ELf(EMI, Waste, Local, Plant)
• Emissions Equation
• EMIf(EL, Other Policy, Cost, Ownership)