V#34 Monte Carlo Simulation of Two Stage Least Square, Instrumental Variable, OLS using Excel
Channel: Zahid Asghar
Date: 07/12/2020

V#29 to V#33 are on Instrumental Variable Regression with concepts and empirical analysis using STATA and R
Link for spreadshet is http://www3.wabash.edu/econometrics/index.htm

Unlike the single-equation model in which a dependent (y) variable is a function of independent (x) variables, other y variables are among the independent variables in each SEM equation. The y variables in the system are jointly (or simultaneously) determined by the equations in the system.

Compare the usual single equation DGP,

,

to a simple, two-equation SEM:

.

Notice that the first equation in the system has a conventional x variable, but it also has a dependent variable (y2) on the right-hand side. Likewise, the second equation has a dependent variable (y1) as a right-hand side variable. In a simultaneous equations system, variables that appear only on the right-hand side of the equals sign are called exogenous variables. They are truly independent variables because they remain fixed. Variables that appear on the right-hand side and also have their own equations are referred to as endogenous variables. Unlike exogenous variables, endogenous variables change value as the simultaneous system of equations grinds out equilibrium solutions. They are endogenous variables because their values are determined within the system of equations.Link for the source of Excel and Ms Word Notes
http://www3.wabash.edu/econometrics/EconometricsBook/chap24.htm
A natural question to ask is, What happens if we just ignore the simultaneity? Suppose, for example, we are interested only in the effect of y1 on y2. Could we simply toss out the first equation and treat the second one as a standalone, single equation, using our usual ordinary least squares regression to estimate the coefficients? In fact, this is what most single-equation regressions actually do – they simply ignore the fact that many x variables are not truly exogenous, independent variables. Unfortunately, it turns out that closing your eyes to the other equations is not a good move: the single equation OLS estimator of ? 1 is biased. This important result, called simultaneity bias, occurs because y1 is correlated with e2