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Understanding Two-Stage Least Squares (2SLS) Estimation in Econometrics

This lecture explores the concept of Two-Stage Least Squares (2SLS) estimation, emphasizing its role in providing unique estimates when using over-identified equations. The methodology allows analysts to utilize all information within a data set by incorporating exogenous variables, thereby enabling precise instrumental variable estimation. We will also delve into the matrix form of 2SLS, examine a practical example involving the Menges Equation, and analyze the significance of various statistical outputs, such as R-square and standard errors.

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Understanding Two-Stage Least Squares (2SLS) Estimation in Econometrics

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  1. 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 identificationInstrumental 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 = 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

  10. Alternative derivation of 2sls

  11. Alternative estimator

  12. 2sls

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