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

2. 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.

3. Understanding identification Instrumental Variable estimation

4. Supply in matrix form

5. 2-stage least squares

6. 2-Stage least squares

7. 2-stage least squares

8. Example

9. 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 = R-SQUARE ADJUSTED =
VARIANCE OF THE ESTIMATE-SIGMA**2 =
STANDARD ERROR OF THE ESTIMATE-SIGMA =
SUM OF SQUARED ERRORS-SSE=
MEAN OF DEPENDENT VARIABLE =
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
YLAG E
I E E
CONSTANT E

10. Alternative derivation of 2sls

11. Alternative estimator

12. 2sls