Which empirical application to use?

[paul-opheim]

Three Current Sets of Results (permalink):

1. Govt Share of Health Exp's impact on life expectancy with GDP/Econ controls (p.8)
2. Govt Share of Health Exp's impact on life expectancy with Gini/Inequality controls (p.9)
3. GDP share of Health Exp's impact on life expectancy with GDP/Econ controls (p.10)

@marionoro 's take The way I see it, we should just do any application where:

1) X and Z are correlated 2) There is a decently complete dataset 3) Z can be described with several variables that all could be viewed as measuring the true Z but with measurement error

I think the life expectancy on Health Spending as Percent of GDP would fit the three criteria, so I vote we just use that. If someone thinks that one of the other two options also meets the three criteria, I am fine with that as well.

[ijyliu]

Points to consider:

• I feel like govt share of health exp's impact on life exp with gini controls is a less interesting question than the others, it's not obvious to me why Ginis are something to control for. I do feel like govt share and ginis are likely to be correlated, so there's that. But why would gini affect life expectancy directly? Not clear. This was kind of just a random regression.
• I really think we will want to eventually add an instrument to both the simulation and the application, given we have the nice theoretical framework we have set up. Obviously it will be hard to find an instrument for GDP. IDK if it is hard or easy to find one for Ginis/inequality, but I don't think it will be easy since it's still a big/complicated macro-level variable subject to 'everything affects everything'
• Difference in results for throwing in all the covariates versus PCA is of similar magnitude but of different direction in all three. I don't know about the literature/expected signs really but we should check.
• Fixed effects make everything insignificant in all three. Seems problematic. I think we might need a longer time period, I doubt there is enough variation in the very few years we end up using (I looked and only 2012-2018 or something had fully nonmissing data). Maybe we can relax the number of variables to get more countries and years.
• As for @marionoro 's criteria, I think X and Z are correlated in all three, the data available is very similar in all three (though more deficient for the Ginis- though we could fix this by including fewer Ginis/mismeasurements), and the case for Z actually being a mismeasurement is strongest for the Ginis, rather than 'economic indicators' which feels more like a latent variable.

[paul-opheim]

From your comments here, it seems like we should use the "economic output" ones and not the Ginis. So "GDP share of Health Exp's impact on life expectancy with GDP/Econ controls" (#3) is the best option. We can decide later if/how we want to do IV, but I think for now we should not spend time on it and just complete a first draft without using IV.

[ijyliu]

@nicomarto what do you think

also there might be another approach to IV where you just instrument the mismeasured variables on each other, that would be easier to implement https://github.com/ijyliu/ECMA-31330-Project/issues/13#issuecomment-836741913

could even combine this with what bonhomme suggested and use several instruments/mismeasurements and then some kind of dimension reduction

[nicomarto]

@ijyliu I agree with @marionoro , since we know how the application works for IV from before, adding that stuff at the end should not be too difficult. Also, once we understood completely whats going on under PCA, applying it to Bonhomme's suggestion should not be too hard

[ijyliu]

Choosing between:

Govt Share of Health Exp's impact on life expectancy with GDP/Econ controls (p.8)
GDP share of Health Exp's impact on life expectancy with GDP/Econ controls (p.10)

I personally find the first, govt share, a more interesting question. The second also feels more dodgy because you are using a GDP share while also controlling for GDP (though not necessarily clear why this would cause problems, it feels kind of unnecessary to have the controls). But please, let's continue the debate

[paul-opheim]

Yeah govt share sounds good to me, so long as govt share of health expenditure seems to have a nonzero covariance with the economic development variable (as judged by looking at its covariances with our various measurements of economic development).

[ijyliu]

On p.15 it looks like it's linked with GDP though not really the other stuff (bottom row)

[paul-opheim]

Is Health spending as percent of GDP on that chart? I don't really know what each label means.

[ijyliu]

Yeah, it's the 9th row, seems less correlated with GDP. but more correlated with official develeopment assistance/foreign aid. Basically anything with GDP in the name is GDP related

Here's a list of the variable names. In future we will definitely label them better, just didn't do that yet since they aren't finalized https://github.com/ijyliu/ECMA-31330-Project/blob/main/Input/wb_indicators_list.csv

[paul-opheim]

Ah, I see now. Let's do the one you wanted then (government share of health spending).

[ijyliu]

ok @nicomarto any thoughts before finalizing this?

[nicomarto]

I agree with the govt share of expenditure. Nevertheless, if results are not that nice, I think we may explore the following option: take the log of percapita spending in health, and all variables in log. May be things may be clearer there (specially because with PCA we dont care about the scale).

Also, we may also run some factor-augmented regression given that factor components is the general case

[nicomarto]

Ok guys, second thought: if we are doing % expenditure on health care, % exp may be constant if GDP and total exp on health grow at the same rate. If so, the per-capita health expenditure will be increasing, which I expect may increase the life expectancy at birth. So, by using % exp we are not capturing the effect of increase expenditure on real terms.

When doing the % exp thing, we are looking at the effect of changes of relative expenditure in health, while I think it makes more sense to capture the effects of real expenditure in health.

[ijyliu]

Ok guys, second thought: if we are doing % expenditure on health care, % exp may be constant if GDP and total exp on health grow at the same rate.

I think that only would apply if we are looking at health share of gdp, not govt share of health? And we were leaning towards govt share?

[ijyliu]

I will make a note in a separate issue about logging things

[nicomarto]

I think that only would apply if we are looking at health share of gdp, not govt share of health? And we were leaning towards govt share?

Yes and no. What if Govt budget drops to a third but govt expenditure drops by a half? You would have an increase in the % of gov spending on health, but a decrease in govt spending on health care. Imagine that that 50% drop in govt spending on health means that half of the public hospital closed. If so, I would expect a decrease in life expectancy while govt share of exp in healthcare is increasing

[ijyliu]

To be clear, the question I find interesting/the point (IMO) of regressing life expectancy on the government's share of overall health spending in a country is seeing if like, for example, public versus private oriented health care systems have better life expectancy. And we are doing this while controlling for overall GDP, which one might think could be linked to higher/lower government shares and also of course directly to life expectancy.

[nicomarto]

Ok. So the idea is to say something like "the higher the share of health expenditure on govt hands, the lower the life expectancy all else equal (i.e private sector may be more efficient in spending, which is not trivial)"? Then we should control for overall GDP pc

[ijyliu]

Yeah basically. The results show a positive correlation between govt share and life expectancy at the moment tho.

It’s clear from that correlation matrix that govt share and gdp are correlated. So then we argue that gdp is a possible confounder increasing life expectancy directly

On Thu, May 20, 2021 at 3:45 PM nicomarto @.***> wrote:

Ok. So the idea is to say something like "the higher the share of health expenditure on govt hands, the lower the life expectancy all else equal (i.e private sector may be more efficient in spending, which is not trivial)"? Then we should control for overall GDP pc

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[ijyliu]

Do we want something with a non-panel structure? Because if it's a panel then maybe this doesn't seem too different from a case where you would use a factor method to deal with noise. Though here it's more random noise, not persistent

(been thinking about the homework, like 1.3)

[paul-opheim]

Personally, I think we should just keep it simple and use the data formatting that we already have.

[ijyliu]

Ok, for the moment I'm going to move forward regressing life expectancy on the govt share of health spending with the economic indicators as controls. We can always come back to this issue and look at the permalink at the top of the page to see the results if we have second thoughts.