PS 233

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PS 233

• Intermediate Statistical Methods
• Lecture 21
• Coping with Endogeneity

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Pervasive Endogeneity Problems

• Endogeneity is one of most pervasive problems in
  social science research
• Fundamental problem is the lack of experimental
  data
• Causes can almost always be effects
• Most common response is to ignore this problem
• We can do better than that!

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Examples of Ignored Endogeneity

• Trade is a cause of international peace
• ORstates trade if they anticipate peace
• Democracy causes economic growth
• OReconomic growth causes democracy
• Campaign money causes candidates to win elections
• ORdonations go to anticipated winners

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Why Is Endogeneity a Problem?

• We have equation YXBe
• We observe covariation between X and Y
• We attribute this covariation to B the impact
  of X on Y

X
B
Y
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The Causal Indeterminacy of Covariation

• But if Y may also be a cause of X, how are we to
  assess the overlap of X and Y
• Should covariation be attributed to B, or a
  second coefficient C reflecting the impact of Y
  on X?

X
Y
C/B
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Imagining a System of Equations

• Now to describe our theory we need a system of
  two or more equations
• Y1 and Y2 are endogenous variables in this
  system and X1-X3 are exogenous

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The Consequences of Ignoring the System

• What happens if we treat these equations as if
  they were not related?
• Estimate bs for first equation
• Y2 is not fixed, it is a function of e2
• Thus we create omitted variable bias

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Showing b is Biased

• Lets examine what b is if we ignore our system
  of equations
• YXbe1, where b(XX)1XY

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Showing b is Biased

• But we know that X is also a cause of Y
• That is, XYce2
• Thus unless cov(e1,e2)0,
• Thus the expectation of b remains

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The Sources of Endogeneity Bias

• Thus the size and direction of endogeneity bias
  is a function of the covariance between e1 and e2
• IF X causes Y and Y also causes X, but the error
  terms are not correlated across these equations,
  we can analyze the equations separately
• BUTthis scenario is quite unlikely

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When Do We Estimate Endogenity?An Example from
Public Opinion
Demographics (Age, Race, Gender)
Party Identification
Education
Tolerance For Casualties
US Right to Attack
US Will Succeed
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Solutions to Endogeneity Bias

• There are two major strategies for coping with
  endogeneity
• First, define and measure observations so as to
  avoid endogeneity
• Specify the endogenous system and account for the
  covariance of e1 and e2 in the estimation
• Today well focus on first strategy

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Do Experimental Research

• Endogeneity bias illustrates one of the great
  strengths of experimental research
• Think about whether your causal mechanism could
  be addressed through experiments
• Could be used in combination with other types of
  real world data

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Reconceptualize the Dependent Variable

• Is part of the dependent variable NOT a cause of
  any independent variables?
• Example Coercive success and crisis outcomes
• Select aspect of Y that is temporally subsequent
  to X
• It falls to researcher to identify what are
  possible causes and possible effects

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Reconceptualize the Independent Variables

• Similar strategy may work with regard to the
  independent variables
• Fundamental strategy is to disagregate data
  narrow unit of observation
• Is there some aspect of X that cannot be a
  consequence of Y?
• Again, it falls to the researcher to identify
  possible causes and effects

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Select Cases without Endogeneity Problems

• Identify cases where exogenous shock alters the
  values of X
• Example Redistricting and the incumbency
  advantage
• This is the quasi-experiment method
• Key problem ensuring the shock is really
  exogenous

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The False Hope of Lagged Variables

• May try to resolve problem with a simple lagging
  of X variables
• Relies on temporal requirements of causality
• Not very effective with time-series data
• Temporal correlations among data mean that et-1
  (or et-5) are likely to be correlated with et

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The Instrumental Variables Approach

• Alternative is to try to address the system of
  equations explicitly
• To estimate our first equation with the bs
  unbiased, we need an estimate of Y2 that is
  independent of e2

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The Instrumental Variables Approach

• We create an instrumental measure of Y2 that is
  purged of its relationship to e2
• Then we can insert this instrumental measure into
  the first equation and proceed to estimate
• More on this solution next time!