# Endogeneity issue in time series model

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 $X$.

• Thank you for you answer. Regards to your first example (exogeneity), however, weather might be have some seasonally effects on consumption, let's say consumptions of beer & ice cream, or unbrella. For you 2nd example, I would say X denotes the development of technology. In the past we do not have any e-devices (iPad, iPhone, etc. ), which didn't impact our consumption. But now as the development of technology, the relevant consumption are increased. Sorry I would have another question ( let's see the next comment). Apr 22, 2016 at 10:34
• (Following the previous comment) Let's assume an equation: Y=a0+a1income+a2consumption+a3employment+u, where Y denotes the consumption to income ratio. Following your 3rd example, is this equation simultaneity? Thank you. Apr 22, 2016 at 10:40
• Weather is exogenous because if it can be expected to affect your consumption, reverse causality seems far-fetched: your consumption today affects the weather tomorrow? I don't think so. For sequential exogeneity: realizations of $X$ do not depend on future realizations of $Y$ (i.e. expectations over future consumption levels) Apr 22, 2016 at 12:35
• For sequential exogeneity: realizations of $X$ do not depend on future realizations of $Y$ (i.e. expectations over future consumption levels)For your equation, it is much worse than endogeneity: Y is consumption/income and you regress on both consumption and income. Why would you do that? Apr 22, 2016 at 12:41
• actually this is not an equation, i just make an assumption following the first discussion which I quoted in my question. Apr 22, 2016 at 14:45