Question

What is the pupose of the two stage least square (TSLS) estimation?Explain using words and equations how it works?In other for the TSLS estimate to be valid,what criteria do the included variables have to satisfy?what happens if each is not satisfied?

Answer 1

This procedure calculates the two-stage least squares (TSLS) estimate. This method is used fit models that include instrumental variables. TSLS includes four types of variable(s): dependent, exogenous, endogenous, and instrument. These are defined as follows:

Dependent Variable: This is the response (or Y) variable that is to be regressed on the exogenous and endogenous (but not the instrument) variables.

Exogenous Variables: These independent variables are included in both the first and second stage regression models. They are not correlated with the random error values in the second stage regression.

Endogenous Variables: Each endogenous variable becomes the dependent variable in the first stage regression equation. Each is regressed on all exogenous and instrument variables. The predicted values from these regressions replace the original values of the endogenous variables in the second stage regression model.

Instrument Variables: Each endogenous variable becomes the dependent variable in the first stage regression equation. Each is regressed on all exogenous and instrument variables.

The 2SLS model is comprised of the following two linear regression models:

$y= \ss _{0} + \ss _{1} + u$