Abstract
The paper considers the OLS, the IV, and two method-of-moments estimators, MM and MMK, of the coefficients of a single equation, where the explanatory variables are correlated with the disturbance term. The MM and MMK estimators are generalizations of the LIML and LIMLK estimators, respectively.
Multivariate first-order approximations to the distributions are derived under normality, using a parameter sequence where the number of instruments increases as the number of observations increases. Numerical results show these approximations are more accurate, compared to large-sample approximations, even if the number of instruments is small.
The moments of the multivariate limit distributions of the MM and MMK estimators can be consistently estimated under a variety of parameter sequences, including the large-sample sequence. The new approximate confidence regions perform well in terms of exact levels, compared to traditional ones.
The IV estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator, which is dominated, in practical cases, by the MM and MMK estimators in terms of nearness to the true value in the sense of Pitman.
Original language | English |
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Pages (from-to) | 657-681 |
Number of pages | 25 |
Journal | Econometrica |
Volume | 62 |
Issue number | 3 |
DOIs | |
Publication status | Published - May-1994 |
Keywords
- INSTRUMENTAL VARIABLES
- METHOD OF MOMENTS
- LIMITED INFORMATION MAXIMUM LIKELIHOOD
- ASYMPTOTIC DISTRIBUTIONS
- PARAMETER SEQUENCE
- SHRINKAGE ESTIMATOR
- PITMAN NEARNESS
- MONTE-CARLO EXPERIMENTS
- SIMULTANEOUS EQUATION SYSTEM
- ASYMPTOTIC EXPANSIONS
- ECONOMETRICS
- LIML