I have two questions regarding the endogeneity issue in linear regression
Endogeneity is a common problem in the linear regression models, but I came across many cases where it is ignored in time series regression. Is the endogeneity problem less serious for time series than cross-section?
I think in some cases, the endogeneity can be less effective as the relationship between two variables can be time-variant. For example, if you have an independent variable that you suspect to be affected by the dependent variable, but it might not be the case at some time points at which the independent variable is not affected by the dependent variable. An example of this can be seen in the relationship between the local asset price and foreign investment flows, the latter can be sometimes driven by returns of the local asset or exogenously driven by other factors. In this case, using time-varying coefficient regression can be helpful to show the points at which the variables are mutually affecting each other.
Is the endogeneity problem naturally redeemable by using time-varying coefficient regression models, and thus it is needless to address it by using an instrumental variable?
I'm using a time-varying coefficient regression model to estimate the impact of foreign capital inflows on local asset prices. The literature suggests that a constant increase in asset prices can derive foreign investors in, there are also cases where exogenous factors push foreign investors in and the flows of the latter drive the local asset prices up. The problem is that so far I couldn't find any linear regression model with time-varying coefficients that incorporates the instrumental variable in the estimation process.