instrumental variable regression - general IV estimation Flashcards
when is a parameter said to be identified?
a parameter is said to be identified if different values of the parameter produce different distributions of the data
in instrumental variables regression, what does the identification of coefficients depend on?
it depends on the relation between the number of instruments (m) and the number of endogenous regressors (K)
when are the coefficients said to be exactly identified?
they are said to be exactly identified if m is equal to k so there are just enough instruments to estimate B1,…,Bk
when is a coefficient overidentified?
when the number of instruments is greater than the number of endogenous regressors.
if the coefficients are overidentified what can you then do?
you can test whether the instruments are valid using a test of over identifying restricitions
if the coefficients are under identified what do you need to do in order to estimate the regressors?
you need to get more instruments
what are the general instrument validity assumptions?
1) instrument exogeniety - corr(Z1i,ui=0,…., corr(Zmi,ui)=0
2) instrument relevance : general case, multiple X’s
what are the IV regression assumptions?
1) E(u_i | W_(1,i) ,…, W_(r,i) = 0
2) (Y_i,X_1i, ….,X_ki, W_1i,…..,W_ri,Z_1i,….,Zmi) are iid
3) the X’s, W’s, X’s and Y have non zero finite 4th moments
4) the instruments (Z1i,….Zmi) are valid
under 1 to 4 the TSLS and its t statics are normally distributed and the critical requirement is that the instruments be valid
what is the conditon for W being an effective control variable?
E(ui|Wi,Zi)=E(ui|Wi)
or the conditional mean of ui does not depend on Zi given Wi
KEY: in many applications you need to include the control vairables so that Z is plausibly exogenous/uncorrelated with u
when are the instruments said to be weak?
the instruments are said to be weak if all the π1,…, πm are either zero or nearly zero for the first stage regression
what is the issue of weak instruments?
weak instruments explain very little of the variation in X beyond that explained by the W’s. if the instruments are weak, then the sampling distributions of the TSLS and its T statitic are not normal even with n large
what is the rule of thumb for checking for weak instruments?
if the first stage F statitic is less than 10, then the set of instruments is weak.
what does the first stage F statstic check for?
the first stage F statistic tests that the hypothesis that Z1,…,Zm do not enter the first stage regression
what to do if you have weak instruments?
get better instruments
if you have many instruments, some are probably weaker than others and its a good idea to drop the weaker ones ( dropping an irrelavent instrument will increase the first stage F
if you only have few instruments and all are weak, then you need to do some IV analysis other than TSLS
