Iterative Instrumental Variables Method and Estimation of a Large Simultaneous System

Abstract The estimation method proposed here offers a way to achieve consistent estimates of simultaneous systems for which the number of observations falls short of the number of predetermined variables in the system as a whole. This method, called the iterative instrumental variables (IIV) method, can be described as iterative use of the instrumental variable interpretation of the 2SLS as given by Klein. A discussion is presented on convergence of the iterative procedure and the asymptotic properties of the IIV method. The special case of the OLS start of the iterative procedure is carefully examined. It is argued that the IIV and the 2SLS methods yield estimators with the same asymptotic distribution. An analysis of the asymptotic covariance matrix of the structural coefficients is presented and compared with that given by Basmann for the 2SLS method. Finally, we analyze the results of a test application of the IIV method to an undersized simultaneous system.

[1]  J. Sargan.  THE ESTIMATION OF ECONOMIC RELATIONSHIPS USING INSTRUMENTAL VARIABLES , 1958 .

[2]  T. Haavelmo.  Methods of Measuring the Marginal Propensity to Consume , 1947 .

[3]  H. Theil,et al.  Economic Forecasts and Policy. , 1959 .

[4]  V. Su,et al.  An Econometric Model of Puerto Rico , 1969 .

[5]  Pankaj Sharma,et al.  Alternative Estimators and Predictive Power of Alternative Estimators: An Econometric Model of Puerto Rico , 1973 .

[6]  Dale W. Jorgenson,et al.  Efficient Estimation of Simultaneous Equations by Instrumental Variables , 1971 .

[7]  R. J. Ball,et al.  The Significance of Simultaneous Methods of Parameter Estimation in Econometric Models , 1963 .

[8]  Notes on the Selection of Instruments for Two Stage Least Squares and K Class Type Estimators of Large Models , 1971 .

[9]  H. Theil.  Specification Errors and the Estimation of Economic Relationships , 1957 .

[10]  T. Kloek,et al.  Simultaneous Equations Estimation Based on Principal Components of Predetermined Variables , 1960 .

[11]  R. L. Basmann.  A GENERALIZED CLASSICAL METHOD OF LINEAR ESTIMATION OF COEFFICIENTS IN A STRUCTURAL EQUATION , 1957 .

[12]  Lawrence R. Klein,et al.  An Essay On The Theory Of Economic Prediction , 1971 .

[13]  Simultaneous Estimation Methods for Large- and Medium-size Econometric Models , 1971 .

[14]  R. Fair.  Efficient estimation of simultaneous equations with auto-regressive errors by instrumental variables , 1972 .

[15]  L. Klein.  ON THE INTERPRETATION OF THEIL'S METHOD OF ESTIMATING ECONOMIC RELATIONSHIPS , 1955 .

[16]  H. Theil,et al.  Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations , 1962 .

[17]  Phoebus J. Dkrymes.  A Simplified Structural Estimator for Large‐Scale Econometric Models1 , 1971 .

[18]  H. Wold.  A fix-point theorem with econometric background , 1966 .

[19]  Olav Reiersöl,et al.  Confluence analysis by means of instrumental sets of variables , 1945 .

[20]  Walter D. Fisher,et al.  ESTIMATING A STRUCTURAL EQUATION IN A LARGE SYSTEM , 1971 .

[21]  B. M. Mitchell.  Estimation of Large Econometric Models by Principal Component and Instrumental Variable Methods , 1971 .

[22]  G. S. Maddala,et al.  Interdependent systems;: Structure and estimation , 1970 .