# sumeera's blog  # Three Stage Least Square Method (3 Sls)

Three-stage least squares originated in a paper by Arnold Zellner and Henri Theil (1962) The term three-stage least squares (3 SLS ) refers to a method of estimation that combines system equation, sometimes known as seemingly unrelated regression (SUR), with two-stage least squares estimation. the two-stage least squares (3 SLS) approach for a system of equations, which would estimate the coefficients of each structural equation separately, the three-stage least squares estimates all coefficients simultaneously. It is assumed that each equation of the system is at least just-identified. Equations that are under identified are disregarded in the 3SLS estimation. 3SLS is generally asymptotically more efficient than 2SLS, if even a single equation of the system is mis-specified, 3SLS estimates of coefficients of all equations are generally inconsistent. First, if the structural disturbances have no mutual correlations across equations (the variance-covariance matrix of the system disturbances is diagonal), then 3SLS estimates are identical to the 2SLS estimates equation by equation. Second, if all equations in the system are just-identified, then 3SLS is also equivalent to 2SLS equation by equation. Third, if a subset of m equations is over identified while the remaining equations are just-identified, then 3SLS estimation of the m over-identified equations is equivalent to 2SLS of these m equations. STAGES • Stage 1 gets 2SLS estimates of the model system • Stage 2 uses the 2SLS estimates to compute residuals to determine cross equation correlations. • Stage 3 uses generalized least squares (- GLS) to estimate model parameters. • Consistent and more efficient than single-equation estimation methods