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ENDOGENEITY

ENDOGENEITY. Development Workshop. 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:

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ENDOGENEITY

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  1. ENDOGENEITY Development Workshop

  2. 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 can’t even tell if they are positive/negative/significant, because we do not know the size of bias + no way to estimate the size of bias

  3. Solutions • If X/Y are not very sticky, using past values is enough • Most economic variables are sticky=>instruments: • 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

  4. Example of the power of tests

  5. Example of the power of tests

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

  7. 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 => get fitted values X* • Regress X* on Y => these are your final results • Interpretation problems • Instruments and theories – Acemoglu, Johnson and Robinson 2001 (AER)

  8. 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.

  9. IV in STATA • Syntax in STATA • ivregressy (x1x2x3= z1z2z3z4) 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?

  10. 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,

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