Why Is Endogeneity An Issue In The Context Of A Multiple Regression Models? (Statistics Project Sample)

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Econometrics
Question 2
Why is endogeneity an issue in the context of a multiple regression models?
The problem of endogeneity occurs when there is a violation of the third assumption. That is, an empirical model for which E(ux)≠0 is considered as having an endogeneity problem. In such a model, the estimates of the β's tend to be biased and inconsistent. There are major causes of endogeneity:
1 Omitted variables
2 Measurement error
3 Simultaneity
Omitted viable bias can be corrected by adding proxy variables. In general, endogeneity issues can be corrected by including instrument variables in a model.
* Given the model yi=α+β1x1i+β2x2i+β3x3i+ui test that x3i is endogenous assuming there are two instruments (z1iand z2i for x2i)
The regression model above has two instrumental variables (z1iandz2i) and one exogenous variable which implies that the endogenous variable x3i is over identified.
Assuming that x3i is uncorrelated with the dependent variable, I would try to estimate this equation using the Ordinary Least Squares method. Then I would compare the OLS estimate with the Two Stage Least Squares estimate (TSLS) and determine whether a significant difference exists between the two outcomes. If there would be a significant difference between the two values, then I would conclude that x3i is an endogenous variable. To achieve this, I would begin by estimating the first stage regression:
x3i=α0+α1z1i+α2z2i+α3x1i+vi
Based on the definition, each random instrument is uncorrelated with the random error term ui, then x3i would be uncorrelated with ui, only if vi is uncorrelated with ui. To determine this, I would run a regression using the following OLS:
yi=α+β1x1i+β2x2i+β3x3i+δ1vi+error
Using this equation, we test the hypothesis:
Null hypothesis: δ1=0
Alternative hypothesis: δ1≠0
The test would be conducted using a standard t-test. Rejecting the null hypothesis would mean that x3i is endogenous since vi and ui would be correlated.
* Is it true that all endogenous variables in a system of equations are stochastic?
Yes, all endogenous variables are regarded as stochastic. In data analysis, the endogenous variables are the variables that a researcher is trying to explain. For instance, consumption is a function of income. However, it is known that consumption does not depend on income alone, hence making it an endogenous variable. However, all endogenous variables are based either on such stochastic equations or on identities. Therefore, the claim holds, all endogenous variables are stochastic.
Is it true that stochastic variables in a system are endogenous?
A stochastic variable is a quantity whose value depends on multiple outcomes. However, most stochastic models are based on definite outcomes; such as walking, running, or taking the bus. Little is left to chance in such a model. It is unlikely for a stochastic variable to be prone to errors that result to endogeneity. Thus, based on the argument I refute the above claim that all stochastic variables are endogenous.
Question 4
Explain: The likelihood ratio test for maximum likelihood estimators (like probit and logit models) is analogous to F tests in the linear regression model.
An F-test is a method of moments test used to test all the parameters in a mo...