Instrumental variable with Panel dataset

[Antonio Ferraro]

Hello everyone,
my name is Antonio, I'm new to the forum and only a beginner in the application of econometric techniques. Having said that, please forgive me any missing in the presentation of my model.
I'm trying to estimate the effect of State investments on regional GDP. The model runs over 12 years (2007-2018) and comprises 21 regions for 252 observations overall. Given the endogeneity of investments on GDP, I'm trying to use a historical instrumental variable (nr of beds in healthcare facilities in 1978 per 1000 inhabitants) as a measure of State investments in the past in each region. The problem is, I don't manage to xtivregress on each region individually (id). I tried with a loop but I'm quite sure that I have misspecified the command. I would also like to save the coefficients of each variable inserted in the regression. I'm using random effects and holding constant 10 other variables besides investments. Any help would be highly appreciated. Thank you.

[Dario Maimone Ansaldo Patti]

If you have a panel, i do not understand why you need to loop over each region. If you want to run a regression for each region (by the way are they italian regions? If so why do you have 21 and not 20 regions?), although you do not have enough observations, you can simply use ivregress or ivreg2.

If you want to run a panel data model you should use something like:

xtivreg y x1 x2 (x3=z1), re

where z1 is your instrument. Notice that you have one instrument for one endogenous regressor. Hence, the model is exactly identified and you cannot test for the exogeneity of the variable. Therefore you need to justify your approach grounding it on the literature.

[Antonio Ferraro]

Dear Dario, thank you for your answer. Yes, they are Italian regions. I've taken the two autonomous provinces of Trento and Bolzano separately, for this reason 21 regions.
The code that you wrote is exactly the one I've used, yet I can't infer from the result what effect has undergone region i. This is why I thought of a loop on each id.

[Dario Maimone Ansaldo Patti]

Antonio:

1) i did not see frequently the split of trentino alto Adige in the two provinces. So you may want to check this.

2) honestly, i have not understood what you want to do. If you elaborate a little bit more on your research question would be great. The only thing I understood is that you are going to evaluate the effect of public investments on regional gdp. If I understood correctly you think that investments are endogenous. Public investments could be larger/smaller in regions with small/high GDP to favor convergence among regions. So you want to overcome such a problem using an instrument on the idea that the instrument (observed in the past) affects investments today, but not the GDP today. Your exclusion restriction here is that the instrument in the past affects the investments today, which in turn affect GDP. In such a way you can also establish causality. Said that and assuming that your exclusion restriction is valid, then the command you used/i suggested should work. The only problem, as i I mentioned in my last post, is that the model is exactly identified and, therefore, you cannot test for the endogeneity of public investment. Hence, you need to construct an appropriate story to justify your model. What I did not understood is "I can't infer from the result what effect has undergone region i". What do you mean?

[Antonio Ferraro]

Basically I am exploiting the policy design of the so called "spesa storica" (historical expenditure) to validate my argument. What this design means is that state investments in the regions is based on what the regions have spent in the past. Since this policy design was firstly introduced in the Italian law in 1978, I use the above-mentioned instrument as a measure of state investments in that particular year in each region. This is assumed to be continuous over time, therefore correlated with investments today. Yet, uncorrelated with regional GDP because financial provision in the healthcare sector was centrally administered and more of an output of political and budgetary bargains. Hence, I want to evaluate how much this policy structure is effective in producing economic stimulus in the regions through its effect on GDP. Moreover, one of the other control variables of interest in the regression is what I've called the "disproportionality rate", that is, the difference between state expenditure in region i and its population. This rate should be proportional in the most underdeveloped regions following another Italian law, but it's not. This is why I am interested in the individual regions coefficients. I hope I was clear.