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:

– 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

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

Example of the power of tests

Example of the power of tests

So what about IV

1. Really hard to find instruments2. Good instruments do not need a good theory3. But to be good, correlation needs to be reliable4. Once we find good instrument – run 2SLS5. But remember that p-values may be out of the moon

and there is little we can do to avoid this problem6. If really want to work hard, use alternative tests

(nobody puts them on statistical packages)

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)

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.

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?

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,