Instruments in panel IV regression model

[Federica Di Marcantonio]

Dears

I have a panel of 5 waves. I am trying to assess the impact of an insurance product on welfare (continues variable). Individual can buy the insurance in two different sale windows (spring or autumn) and the insurance cover last in both case for one year (so there is a period of overlap of the insurance coverage). Because the uptake of insurance is considered in the related literature as endogenous I use an IV regression model. As an instrument it is generally used discount coupons (% of discount received to buy the product) so I did the same. However, in my case the instrument turn out to be very weak. I think that while for cross section this instrument works in panel does not because after the first purchase the uptake might be also influenced by good/bad experiences.

So this is my current model:

xtivreg Y X1 X2 X3 ( L.uptake_spring L.uptake_autum= L.discount_spring  L.discount_autum)  , fe

I use the lad because I suppose that the effect of insurance take place once they receive the payout so after 1 year.

So in order to solve the problem I thought to use an combined instrument such as

xtivreg Y X1 X2 X3 ( L.uptake_spring L.uptake_autum= L.discount_spring#badexperience(t)  L.discount_autum)#badexperience(t)  , fe

where for #badexperience(t) I mean the possibility for the person that bought the insurance of not receive a payout (this can happen with the type of product I am studying)

Is that procedure correct/possible?
Does anyone have a different solution for this problem?
Could I use an alternative estimation procedure to model my research question?

Thanks

Federica

[Joao Santos Silva]

Is uptake continuous or a dummy? What about the instruments?

Joao

[Federica Di Marcantonio]

Uptake is a dummy yes/no while for the instruments I have 2 options (a dummy -received or not the coupon- or % of discount coupons (0-10%-25%-45%-55%-65%-70%) ) In my case I have used the continues one.
F.

[Joao Santos Silva]

If the uptake is a dummy, you may want to start to run a logit of uptake on your instruments and exogenous variables and then do 2SLS using the instruments you had before plus the fitted probabilities from the logit; that generally improves the quality of the instruments. This approach was used here (see the top of page 291):

Windmeijer, F. and Santos Silva, J.M.C. (1997), Estimation of Count Data Models with Endogenous regressors; An Application to Demand for Health Care, Journal of Applied Econometrics, 12(3), pp. 281-294.

Best wishes,

Joao

[Federica Di Marcantonio]

Sorry Joao I forgot to thank you for the insights!