Open AccessInstrumental variable estimation with heteroskedasticity and many instruments
Author(s) -
Hausman Jerry A.,
Newey Whitney K.,
Woutersen Tiemen,
Chao John C.,
Swanson Norman R.
Publication year - 2012
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe89
Subject(s) - heteroscedasticity , homoscedasticity , estimator , instrumental variable , econometrics , allowance (engineering) , monte carlo method , range (aeronautics) , mathematics , statistics , economics , engineering , operations management , aerospace engineering
This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve efficiency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has finite moments and high asymptotic efficiency in a range of cases. The standard errors are easy to compute, being like White's (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. We find that the estimator is asymptotically as efficient as the limited‐information maximum likelihood (LIML) estimator under many weak instruments. In Monte Carlo experiments, we find that the estimator performs as well as LIML or Fuller (1977) under homoskedasticity, and has much lower bias and dispersion under heteroskedasticity, in nearly all cases considered.