Hey Karthik, starting separate thread for a different issue. I opened your main spreadsheet for the first time, and I’m not positive but I think the 90% reduction claim is due to a spreadsheet error? The utility gain in B5 that flows through to your bottom line takeaway is hardcoded as being in log terms, but if eta changes than the utility gain to $s at the global average should change (and by the way I think it would really matter if you were denominating in units of global average, global median, or global poverty level). In this copy I made a change to reimplement isoelastic utility in B7 and B8. In this version, when eta=1.00001, OP ROI is 169, and when eta=1.5, OP ROI is 130, for a difference of ~25% rather than 90%. I didn’t really follow what was happening in the rest of the sheet so it’s possible this is wrong or misguided or implemented incorrectly.
You… are absolutely right. That’s a very good catch. I think your calculation is correct, as the utility translation only happens twice—utility from productivity growth, which I adjusted, and utility from cash transfers, which I did not. Everything else is unchanged from the original framework.
You’re definitely right that it matters whether this is global average/median/poverty level. I think that the issue stems from using productivity A as the input to the utility function, rather than income. This is not an issue for log utility if income is directly proportional to A, since it cancels out, but it is probably better to redo this with income statistics/income growth and see how that changes things.
I’ll make a note about this at the top of the post and update it with a more substantive change to the conclusion when I’ve dug into it further.
Hey Karthik, starting separate thread for a different issue. I opened your main spreadsheet for the first time, and I’m not positive but I think the 90% reduction claim is due to a spreadsheet error? The utility gain in B5 that flows through to your bottom line takeaway is hardcoded as being in log terms, but if eta changes than the utility gain to $s at the global average should change (and by the way I think it would really matter if you were denominating in units of global average, global median, or global poverty level). In this copy I made a change to reimplement isoelastic utility in B7 and B8. In this version, when eta=1.00001, OP ROI is 169, and when eta=1.5, OP ROI is 130, for a difference of ~25% rather than 90%. I didn’t really follow what was happening in the rest of the sheet so it’s possible this is wrong or misguided or implemented incorrectly.
You… are absolutely right. That’s a very good catch. I think your calculation is correct, as the utility translation only happens twice—utility from productivity growth, which I adjusted, and utility from cash transfers, which I did not. Everything else is unchanged from the original framework.
You’re definitely right that it matters whether this is global average/median/poverty level. I think that the issue stems from using productivity A as the input to the utility function, rather than income. This is not an issue for log utility if income is directly proportional to A, since it cancels out, but it is probably better to redo this with income statistics/income growth and see how that changes things.
I’ll make a note about this at the top of the post and update it with a more substantive change to the conclusion when I’ve dug into it further.