The endogeneity problem, as it is well known, arises from the simultaneity between the dependent and some independent variables, there are other cases in which endogeneity arises from omitted variables.
One of the effects of endogeneity is that it renders the parameters of the model causally uninterpretable. However, sometimes researchers do ignore presence of endogeneity.
If you run a time series regression model suspecting that there might be implications of endogeneity, would you ignore it if the parameters of your model are fairly and properly interpretable? I would like to see an academic reference that solidifies the proposition of ignoring the endogeneity.
Your second paragraph highlights the challenges associated with the failure to test for endogeneity. I suggest you always test to be sure your model is free from endogeneity.
Hi, this is a key question. When you are interested in forecasting, you can forget about the problem of endogeneity. It is not a question about regression with time series or not, it is a question about predictability or not. It turns out that many papers in time series are about forecasting. Let me elaborate:
Imagine you have the following extremely simple regression model where "e" is an error term:
y =a+bx+cz+e
Let us suppose that you have an endogeneity issue here. Then you know that the OLS estimates of the a,b and c parameters are not consistent...so OLS estimates do not converge in probability to the true vector of parameters (a,b,c).
A fair question to ask is the following: where are the OLS estimates converging to??? the answer is very interesting. OLS estimates converge to another set of parameters that I will denote A, B and C.
These parameters are known as the Best Linear Predictor (BLP) of the variable "y" on the basis of the information contained in the variables "x" and "z". They have this name because if you want to forecast the "y" variable with information contained in the variables "x" and "z" the forecast "A+Bx+Cz" produces the minimum Mean Squared Prediction Error accross all the linear predictors of "y" using "x" and "z".
¿Entiende amigo?
So, OLS estimates are consistent for the model: y=A+Bx+Cz+u
and are inconsistent for the model y=a+bx+c+u
Many papaers about forecasting don´t even mention the problem of endogeneity for the reasons explain above.
Hope it helps!!!!
Thanks Mr. Pablo Pincheira for the detailed answer
As you mentioned the convergence problem that the model would suffer under the endogeneity, I'm wondering if the convergence of the parameters differs depending on the type of the endogeneity. Do the endogeneity implications on the convergence of the parameters differ depending on the type of endogeneity? i.e. the endogeneity that is caused by interdependence between dependent and independent variables, and the endogeneity that stems from the omitted variables which leads to a correlation between the error term and some independent variables.
You might want to see the paper below that distinguishes weak, strong and super exogeneity depending upon the purpose of the analysis. For example, weak exogeneity is required for the valid estimation of parameters in one equation without reference to information provided by another equation. Consumption functions involve the regression of consumption on income (two variables that are intrinsically endogenous), however, consumption is often found to be weakly exogenous with respect to income, making interpretation of the consumption equation (without reference to the income equation in the system) valid.
Robert F. Engle, David F. Hendry and Jean-Francois Richard (1983) Exogeneity
Econometrica Vol. 51, No. 2 (Mar., 1983), pp. 277-304.
Hi Aboubakr Med,
The issue about the convergence is given by the condition E(Xe) being not zero. This is the endogeneity condition, so irrespective of the source of endogeneity you might have, the problem of the convergence to other set of parameters will be the same.
Cheers
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