Lecture 20 Two Stage Least Squares Economics 310 Lecture 20 Two Stage Least Squares

Two Stage Least Squares Want Unique Estimates with over-identified equations Want to use all information in system’s data set. Two stage least squares allows us to use all exogenous variables and still get unique estimates.

Understanding identification Instrumental Variable estimation

Supply in matrix form

2-stage least squares

2-Stage least squares

2-stage least squares

Example

Estimate of 1st Menges Equation |_2sls y ylag i (ylag, clag, qlag, r, p) TWO STAGE LEAST SQUARES - DEPENDENT VARIABLE = Y 5 EXOGENOUS VARIABLES 2 POSSIBLE ENDOGENOUS VARIABLES 51 OBSERVATIONS R-SQUARE = 0.9975 R-SQUARE ADJUSTED = 0.9974 VARIANCE OF THE ESTIMATE-SIGMA**2 = 1750.8 STANDARD ERROR OF THE ESTIMATE-SIGMA = 41.843 SUM OF SQUARED ERRORS-SSE= 84040. MEAN OF DEPENDENT VARIABLE = 7301.2 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 48 DF P-VALUE CORR. COEFFICIENT AT MEANS YLAG 1.0053 0.1125E-01 89.35 0.000 0.997 0.9818 0.9972 I 0.10274E-01 0.4928E-02 2.085 0.042 0.288 0.0319 0.0024 CONSTANT 3.3871 75.70 0.4474E-01 0.964 0.006 0.0000 0.0005

Alternative derivation of 2sls

Alternative estimator

2sls