I ended up getting a lot of feedback (pushback?) on my post regarding culture and economic growth. The TL;DR version is this: if culture influences utility functions, then comparing economic development levels between cultures not very interesting because it doesn't ultimately inform us about welfare.
Several people got back to me about ways that culture could matter for economic development without necessarily implying differences in utility functions. While not doing full justice to each comment, I think the common thread was this: coordination failures.
Perhaps you have some cultural norm that says to distrust strangers. In some kind of repeated dynamic game, your first choice is to deviate/defect/cheat, and this leads to a bad equilibrium where everyone continues to deviate/defect/cheat. This means you do not take advantage of mutually beneficial transactions. In contrast, a culture that says to trust strangers will choose to cooperate as a first choice, and this leads to a good dynamic equilibrium where everyone continues to cooperate (lend to each other, transact with each other, make long-term contracts with each other) and allows for greater economic specialization.
Now, if the cultural norm of distrusting strangers is there to minimize the utility loss (shame?) from being cheated, then its still just a utility function difference, and we can't really say that people are worse off from distrusting strangers. They are, after all, avoiding something that hurts them very badly. But if the cultural norm of distrusting strangers is just some odd historical outcome, then I could see how this cultural norm is really affecting not just economic development, but also welfare. People would like to coordinate on "cooperate" and achieve the good long-run equilibrium, but no one has any incentive to act alone.
That said, cultural norms of distrusting strangers (or trusting them) aren't random. They must have some basis in past cultural experience, and so I'd be worried that it directly influences utility in some manner. But as a general proposition, the idea that culture has an influence on economic development and welfare because of coordination failures seems like a good avenue to pursue.
The idea that culture is tied up with solving coordination problems runs through a lot of the work of Avner Greif. His 1994 paper on cultural beliefs and economic outcomes compares an individualist culture (Genoese traders) with a collectivist one (Maghribi traders) in how they dealt with severe principal-agent issues. Summarizing, the Genoese developed a vertical structure that relied on formal institutions to mediate disputes, while the Maghribi developed a horizontal structure that relied on intra-group cooperation to mediate distputes (i.e. punish cheaters).
Greif does not explain why the Genoese or Maghribi adopted these different attitudes, he just documents that the choice of vertical versus horizontal structure makes sense given their cultural attitudes. He's also clear about ranking these systems:
Hence although in the long run the Italians drove the Muslim traders out of the Mediterranean, the historical records do not enable any explicit test of the relative efficiency of the two systems (p.942-43)
So it's not immediately obvious whether the collectivst culture was worse for economic outcomes (perhaps the Genoese had other advantages we don't know about). But to my prior point, even if the collectivist culture was demonstrably worse for the economic outcomes, we don't know anything about how individualism and collectivism entered the utility functions of these groups. Hence we don't know whether the Genoese or the Maghribi were better off with their system.
The one way I see that you could definitively argue that the collectivist culture was "worse" was if the Genoese and Maghribi shared a common utility function, and the move to collectivism by the Maghribi was the result of a random historical event unassociated with that utility function. By random I mean, if we re-ran world history 1000 times, then in about half of them we should see the Genose ending up with collectivist institutions and the Maghribi with individualistic ones.
That seems like a tall order. I'd be shocked if the Maghribi's collectivist culture, and hence adoption of a horizonatal structure that (might have) had a detrimental effect on their economy, was just random noise.
Obviously world history didn't start with the Genoese and Maghribi, and their predisposition for collectivism and individualism was the result of historical events leading to that specific time and location. So perhaps there were a series of random occurrences over history that snowballed into the collectivist culture of the Maghribi and the individualist of the Genoese.
Which is a long way of saying that countries could share a common utility function (making GDP or income comparisons meaningful), have different cultures due to a series of historical contingencies, and that those cultural traits could have meaningful economic effects because of how they influence coordination problems. In that case, then it would be meaningful to talk about culture's effect on GDP, because culture is essentially capturing some kind of historical path dependence.