Points all well-taken. I’d love to share with FP’s journal club, though I hasten to add that I’m still making edits and modifications based on your feedback, @smclare’s, and others.
With respect to uncertainty in the CE calculation, my thinking was (am I making a dumb mistake here?) that because
Var(XY)=E(X2Y2)−E(XY)2 and Cov(X2Y2)=E(X2Y2)−E(X2)E(Y2) , then Var(XY)=Cov(X2,Y2)+E(X2)E(Y2)−E(XY)2. So if covariance is nonzero, then (I think?) the variance of the product of two correlated random variables should be bigger than in the uncorrelated counterfactual.
To me, the main value of the CE model was in the sensitivity analysis—working through it really helped me think about what “effective lobbying” would have to be able to do, and where the utility would lie in doing so. I think if it doesn’t serve this purpose for the reader, then I agree this document would have been better off without the model altogether.
Thanks for your thoughts on money in politics. Vis (1) I have to think more about this, but I do definitely view the topic a little differently. For instance, it’s not obvious to me that economic arguments and political representation do the necessary work of regulatory capture. Boeing is in Washington and Northrop Grumman is in Virginia. It seems clear that the representatives of the relevant districts are prepared to argue for earmarks that will benefit their constituents… but these companies are still in direct competition, and it seems like there’s still strategic benefit to each in getting the rest of Congress on their side. I might misunderstand- maybe we’re reaching the limits of asynchronous discussion on this topic.
Vis (2), the “inside view” I was talking about was actually yours, as someone who thinks about this professionally- so thank you for your thoughts!
1) I don’t see incompleteness as an issue—what is good for Journal Club is bringing in lots of interesting ideas which your post certainly does, updates you made and are working on are fine. So if that would work for you, I would suggest you as a speaker for Journal Club and we could see when it would fit over the next month or so?
2) My reading of your model—which might be wrong—was that you assumed independence between variables related to cost/effort and variables of success probability. It seems to me that when they are positively correlated rather than independent, cost efficiency would increase and become more narrow, because what this says is that worlds of high spending and success will be more likely to co-occur and worlds of high spending and no success less likely to occur than under independence. Does this make sense?
3) I think on money in politics my understanding is that a couple of intensely motivated politicians—e.g. the representatives where headquarters of companies are—can be quite sufficient for pork barrel style politics because they tend to fill committee positions important for their respective economic interests and they can easily bargain with other legislators.
1) Sounds good to me! We can connect about it over DM.
2) Your reading is right. A priori, a positive correlation means lower cost-effectiveness in expectation. However, I’m not sure if it means anything generally for the median cost-effectiveness (which I tried to work with in my existing CEA), irrespective of the other model parameters. And in my existing setup, if worlds of high spending and high success are more likely co-occur, and worlds with low spending and low success are more likely to co-occur, then I believe the distribution of their product would have been more dispersed, since there would be more values at the extremes (high/high and low/low) then there would be if they were independent. But I’m pretty convinced now that a better approach would have been, as you’ve suggested, to do separate CEAs conditional on various assumed interventions. Rather than change the parameters of independent distributions as I did in the posted analysis, the true next step is probably to re-model under varying assumptions about the covariance of the different variables.
3) I have a different sense of this, but not an overwhelmingly different sense, and I’m going to think about it some more.
Points all well-taken. I’d love to share with FP’s journal club, though I hasten to add that I’m still making edits and modifications based on your feedback, @smclare’s, and others.
With respect to uncertainty in the CE calculation, my thinking was (am I making a dumb mistake here?) that because
Var(XY)=E(X2Y2)−E(XY)2 and Cov(X2Y2)=E(X2Y2)−E(X2)E(Y2) , then Var(XY)=Cov(X2,Y2)+E(X2)E(Y2)−E(XY)2. So if covariance is nonzero, then (I think?) the variance of the product of two correlated random variables should be bigger than in the uncorrelated counterfactual.
To me, the main value of the CE model was in the sensitivity analysis—working through it really helped me think about what “effective lobbying” would have to be able to do, and where the utility would lie in doing so. I think if it doesn’t serve this purpose for the reader, then I agree this document would have been better off without the model altogether.
Thanks for your thoughts on money in politics. Vis (1) I have to think more about this, but I do definitely view the topic a little differently. For instance, it’s not obvious to me that economic arguments and political representation do the necessary work of regulatory capture. Boeing is in Washington and Northrop Grumman is in Virginia. It seems clear that the representatives of the relevant districts are prepared to argue for earmarks that will benefit their constituents… but these companies are still in direct competition, and it seems like there’s still strategic benefit to each in getting the rest of Congress on their side. I might misunderstand- maybe we’re reaching the limits of asynchronous discussion on this topic.
Vis (2), the “inside view” I was talking about was actually yours, as someone who thinks about this professionally- so thank you for your thoughts!
Hi Matt,
1) I don’t see incompleteness as an issue—what is good for Journal Club is bringing in lots of interesting ideas which your post certainly does, updates you made and are working on are fine. So if that would work for you, I would suggest you as a speaker for Journal Club and we could see when it would fit over the next month or so?
2) My reading of your model—which might be wrong—was that you assumed independence between variables related to cost/effort and variables of success probability. It seems to me that when they are positively correlated rather than independent, cost efficiency would increase and become more narrow, because what this says is that worlds of high spending and success will be more likely to co-occur and worlds of high spending and no success less likely to occur than under independence. Does this make sense?
3) I think on money in politics my understanding is that a couple of intensely motivated politicians—e.g. the representatives where headquarters of companies are—can be quite sufficient for pork barrel style politics because they tend to fill committee positions important for their respective economic interests and they can easily bargain with other legislators.
1) Sounds good to me! We can connect about it over DM.
2) Your reading is right. A priori, a positive correlation means lower cost-effectiveness in expectation. However, I’m not sure if it means anything generally for the median cost-effectiveness (which I tried to work with in my existing CEA), irrespective of the other model parameters. And in my existing setup, if worlds of high spending and high success are more likely co-occur, and worlds with low spending and low success are more likely to co-occur, then I believe the distribution of their product would have been more dispersed, since there would be more values at the extremes (high/high and low/low) then there would be if they were independent. But I’m pretty convinced now that a better approach would have been, as you’ve suggested, to do separate CEAs conditional on various assumed interventions. Rather than change the parameters of independent distributions as I did in the posted analysis, the true next step is probably to re-model under varying assumptions about the covariance of the different variables.
3) I have a different sense of this, but not an overwhelmingly different sense, and I’m going to think about it some more.