ENDOGENEITY

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ENDOGENEITY

• Development
• Workshop

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What is endogeneity and why we do not like it

• Three causes
• X influences Y, but Y reinforces X too
• Z causes both X and Y fairly contemporaneusly
• X causes Y, but we cannot observe X and Z (which
  we observe) is influenced by X but also by Y
• Consequences
• No matter how many observations estimators
  biased (this is called inconsistent)
• Ergo whatever point estimates we find, we cant
  even tell if they are positive/negative/significan
  t, because we do not know the size of bias no
  way to estimate the size of bias

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Solutions

• If X/Y are not very sticky, using past values is
  enough
• Most economic variables are stickygtinstruments
• Easy use lag of X instead of X as its instrument
  (only if not very sticky)
• Hard find an adequate instrument, i.e. variable
  uninfluenced by Y that correlates well with X
• Few words about instruments and their quality
• (paper by Frank Kleibergen, Econometrica, 2002)
• Method find instruments, run 2SLS, trust your
  results
• Problem t-test and F-test may loose power under
  2SLS
• In other words estimators are fine, standard
  errors are fine, but the tests we use for them
  behave far from normal

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Example of the power of tests
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Example of the power of tests
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So what about IV

1. Really hard to find instruments
2. Good instruments do not need a good theory
3. But to be good, correlation needs to be reliable
4. Once we find good instrument run 2SLS
5. But remember that p-values may be out of the moon
   and there is little we can do to avoid this
   problem
6. If really want to work hard, use alternative
   tests (nobody puts them on statistical packages)

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IV method

• Variables X and Y expected to be endogenous
• Z correlates well with X (purely statistical
  property) and by definition cannot depend on Y
• Z is called an instrument
• Regress Z on X gt get fitted values X
• Regress X on Y gt these are your final results
• Interpretation problems
• Instruments and theories Acemoglu, Johnson and
  Robinson 2001 (AER)

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IV method

• One needs as many equations as endogenous
  variables
• For each endogenous variable one needs one
  (separate for each) instrument
• For each first stage regression one can use the
  same instruments as well.

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IV in STATA

• Syntax in STATA
• ivregress y (x1 x2 x3 z1 z2 z3 z4) x4 x5 x6
• We run a regression in which
• y is explained
• x1, x2, x3 are endogenous (instrumented for)
• z1, z2, z3 are exogenous (instruments)
• x3, x4 x5 are exogenous too (do not need to be
  instrumented)
• Difference between automatic and manual 2SLS?

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Papers

• Ann Harrison, Opennes and growth A time-series,
  cross-country analysis of developing countries,
  Journal of Development Economics, 1996
• Jeffrey Frankel i David Romer, Does Trade Cause
  Growth?, AER 1999
• Jeffrey Frankel i Andrew K. Rose, One Money, One
  Currency,