Instrumental Variable: Does including past values of regressors into the IV cause exogeneity assumption to fail?

[Karl Kiesinger]

Setup: Annual panel of 125 countries. I am interested in the effect of x on y. As an instrument z I use an interaction of the variables gamma and delta. gamma fulfils the conditions of relevance and exogeneity. delta is the country’s propensity to receive x, which is an indicator variable based on how much x the country received in the past.
Question: Assuming that x in the past is correlated with today’s y – would then my instrument fail to comply with the exogeneity condition because through delta my instrument explains part of the variation in y (which is not through today’s x)?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I'm not sure of your precise model, but I think the general answer is that it depends on how the serial correlation works in your data. If you have errors correlated over multiple lagged values, then that may make lagged dv's endogenous. Many assume one lag of the serial correlation making an extra lag OK.

[Karl Kiesinger]

Thank you for your recommendations. I didn’t provide stata material because it doesn’t exist yet. I will do that in the future though.

I am sorry I am quite new to this, so I don’t fully understand your answer. Do you mean if the propensity score would be based on periods that are more than one period in the past, I “overcome the serial correlation” and therefore don’t have the problem of violating the exogeneity condition?