CHAPTER 20: SIMULTANEOUS-EQUATION METHODS

ü  Approaches to Estimation

·         Single-equation methods/limited information methods

·         Systems methods/full information methods

Single-equation methods:

1.      Ordinary Least Squares (OLS)

2.      Indirect Least Squares (ILS)

3.      Two-Stage Least Squares (2SLS)

ü  Recursive Models and Ordinary Least Squares

Zero contemporaneous correlation – same-period disturbances in different correlations are uncorrelated.

ü  Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS)

Step 1: We first obtain the reduced-form equations.

Step 2: We apply OLS to the reduced-form equations individually.

Step 3: We obtain estimates of the original structural coefficients from the estimated reduced-form coefficients obtained in Step 2.

ü  Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS)

Stage 1: To get rid of the likely correlation between Y₁ and u₂, regress first Y₁ on all the predetermined variables in the whole system, not just that equation.

Stege 2: The overidentified money supple equation can now be written as:

Y_2t = β_2t + β_2tY_1t + u_t

Features of 2SLS:

1.      It can be applied to an individual equation in the system without directly taking into account any other equation(s) in the system.

2.      Unlike ILS, which provides multiple estimates of parameters in the overidentified equations, 2SLS provides only one estimate per parameter.

3.      It is easy to apply because all one needs to know is the total number of exogenous or predetermined variables in the system without knowing any other variables in the system.

4.      Although specially designed to handle overidentified equations, the method can also be applied to exactly identified equations.

5.      R² values in the reduced-form regressions are very high, the classical OLS estimates and 2SLS estimates will be very close.