Choosing the Number of Instruments

Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross-section applications. In this paper we address this problem by deriving simple mean-square error criteria that can be minimized to choose the instrument set. We develop these criteria for two-stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean-square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.

[1]  Takamitsu Sawa,et al.  Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate , 1979 .

[2]  Thomas M. Stoker,et al.  Optimal bandwidth choice for density-weighted averages , 1996 .

[3]  J. Stock,et al.  Instrumental Variables Regression with Weak Instruments , 1994 .

[4]  J. Angrist,et al.  Does Compulsory School Attendance Affect Schooling and Earnings? , 1990 .

[5]  Paul A. Bekker,et al.  ALTERNATIVE APPROXIMATIONS TO THE DISTRIBUTIONS OF INSTRUMENTAL VARIABLE ESTIMATORS , 1994 .

[6]  A. L. Nagar.  The Bias and Moment Matrix of the General k-Class Estimators of the Parameters in Simultaneous Equations , 1959 .

[7]  H. James.  VARIETIES OF SELECTION BIAS , 1990 .

[8]  Whitney K. Newey,et al.  EFFICIENT INSTRUMENTAL VARIABLES ESTIMATION OF NONLINEAR MODELS , 1990 .

[9]  Ker-Chau Li,et al.  Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set , 1987 .

[10]  T. Rothenberg.  ASYMPTOTIC PROPERTIES OF SOME ESTIMATORS IN STRUCTURAL MODELS , 1983 .

[11]  J. Angrist,et al.  Jackknife Instrumental Variables Estimation , 1995 .

[12]  Wolfgang Härdle,et al.  APPLIED NONPARAMETRIC METHODS , 1992 .

[13]  Donald W. K. Andrews,et al.  Consistent Moment Selection Procedures for Generalized Method of Moments Estimation , 1999 .

[14]  Thomas J. Rothenberg,et al.  Approximating the distributions of econometric estimators and test statistics , 1984 .

[15]  C. L. Mallows.  Some comments on C_p , 1973 .

[16]  W. Newey,et al.  Convergence rates and asymptotic normality for series estimators , 1997 .

[17]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[18]  Joshua D. Angrist,et al.  Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records , 1990 .

[19]  Oliver Linton,et al.  SECOND ORDER APPROXIMATION IN THE PARTIALLY LINEAR REGRESSION MODEL , 1995 .

[20]  David A. Jaeger,et al.  Problems with Instrumental Variables Estimation when the Correlation between the Instruments and the Endogenous Explanatory Variable is Weak , 1995 .

[21]  K. Morimune.  Approximate Distributions of k-Class Estimators when the Degree of Overidentifiability is Large Compared with the Sample Size , 1983 .