Can anybody tell me about endogeneity issue in time series?
I've read one paper, discuss that
income is likely to be endogenous for consumption. However, on the UK
data, the current quarter growth of real income appears to be weakly
exogenous for the long consumption to income ratio.
Also, another one says
the flow of funds into mortgage is determined by financial system,
which is exogenous.
Actually, I knew a little bit about endogenous in a cross-section model, but here I cannot understand why there is endogeneity in a time series model. If the endogeneity issues do exist in a model, when I conduct an ECM model, can I use 2SLS in the long run model?
Endogeneity may arise from various reasons: omitted variable (you forget important controls in your model), measurement error (your data are poor measures of the true variable you're willing to capture), and simultaneity.
In your case, it is probably simultaneity. Simultaneous determination of both variables arise because observed income and consumption are equilibrium outcomes.
Regression models based on time-series require assumptions with regards to the exogeneity of independent variables in a dynamic context, say $X$.
Assume $Y$ is consumption.
(Exogeneity) e.g. X is the weather: past, current and future weather realizations are exogenous to my consumption level $Y$, since my consumption couldn't possibly have a causal effect on sunshines.
(Sequentially Exogeneity) e.g. X is (can't find a good example here?): past and current realizations of X are not caused in any way by my consumption $Y$, but future realizations may be so. If agents are not forward-looking, then income X may not depend on expected future consumption.
(Endogeneity) e.g. X is income: since I could have decided yesterday to work more to increase my income X in anticipation of today's consumption $Y$ (savings to buy a new car), past and current $Y$ may cause current $X$.