The occupational theory implies that Jews came to Europe with an unremarkable mean IQ, got involved in commerce and banking and then got smarter while working in those professions.
One of this theory's assumptions is that banking and commerce select for intelligence more than farming or, say, blacksmithing do. To put it another way, this theory says that intelligence is more useful in commerce than in farming and that the advantage that a smart merchant has over unintelligent ones is greater than the advantage that a smart farmer has over unintelligent farmers.
Is this really true? It could be. The capacity for hard work could be more important than IQ in farming, and the two are not perfectly correlated. For example, it seems to me that in Mexico people of Spanish descent are both smarter and less hard-working than people of Amerindian descent. Southeast Asians and low-caste East Indians are two more examples of hardworking groups with modest mean IQs. Northern Italians are as smart as Germans, but probably less hard-working.
Why did Jews become involved in commerce after coming to Europe? Probably because they were a part of a wide diaspora. They had contacts all over the Mediterranean world and beyond. A wide network of contacts provides an advantage in commerce. OK, but Roman-era slave trade brought lots of Middle Easterners to the European parts of the empire. Pax Romana and good Roman roads led to a general mixing of peoples which created many diasporas. Why did Jews end up as the chief mercantile people of Europe and the Middle East then? Why not some other population?
Well, the other diasporas - Cappadocians, Bythinians, Parthians, etc. - didn't last in Europe. They disappeared when all of their European members accepted Christianity and assimilated into the general Christian melting pot of their particular place of residence.
OK, then why did a lot of Jews stick to their religion while everyone around them abandoned theirs in favor of Christianity or Islam? Most late pagan survivals were in hard-to-access areas like the Afghan and Kurdish mountains, the Caucasus, the Canary Islands, etc. Jews were the only ones who resisted conversion in easily-reached, urban environments. Why?
The fact that Jews were already monotheists when Christianity and Islam appeared on the scene could have been a factor. Monotheism is "stickier" than polytheism. People are more likely to want to fight for it. I'm not aware of any religious wars that were fought before the spread of monotheism, among polytheists. And all of the religious wars that have been fought between monotheists and polytheists (Charlemagne's Saxon campaigns, for example) were ultimately won by monotheists. They seem to have had more motivation. If you think that there's only one God in the Universe, then all other people's Gods will seem false to you. A polytheist might add some foreign God to his pantheon from time to time. A monotheist cannot. From his perspective polytheists and rival monotheists are wrong about the most fundamental issues in the Universe.
One can find historical instances of Jews being converted to Christianity (in 14th and 15th century Spain for example) and Islam (Sabbatai Zevi and his followers). But I think that this sort of thing is harder to do than converting polytheists to monotheism.
Why did monotheism arise among Jews earlier than among most peoples? The earliest known example of monotheism is Akhenaton's Aten cult in Egypt. Surprisingly in light of monotheism's later performance, the Aten cult wasn't sticky. Egyptians reverted to polytheism after Akhenaton's death. Canaan (a part of which later became Judea) was a vassal of Egypt during Akhenaton's lifetime. So its population would have been exposed to the Aten cult. But to a lesser extent than Egyptians. And the particular Jewish version of monotheism was born quite a few centuries after Akhenaten's death. In summary, I don't know why monotheism appeared among Jews earlier than among most peoples. This is where this particular line of inquiry breaks off. So let's start another one.
The Talmudic theory of Jewish intelligence emphasizes the fact that the nature of Judaism changed after the failure of Jewish revolts against Roman authority in the 1st and 2nd centuries AD. The Jerusalem Temple was destroyed and most Jews were exiled from Judea in the aftermath of Roman victory. Proponents of the Talmudic theory say that before this happened Judaism revolved around sacrifices in the Temple. With the Temple destroyed, Judaism found another focus for itself in the study of religious and legal texts.
The Talmud was written after the failure of anti-Roman revolts and partly in exile. Its prose is complex and legalistic. The Talmudic theory of Jewish intelligence claims that over the following centuries those Jews who did not enjoy the close study of complicated legal texts left the religion. Those who liked it and were good at it stayed. It is certainly true that being proficient at the study and interpretation of scripture carries prestige in modern ultra-orthodox Jewish communities. Being descended from famous Talmudic scholars is a point of pride, as is having one's daughter marry one.
The biggest argument for the Talmudic theory is that modern Jewish intelligence is highly verbal and legalistic in nature. The other mercantile peoples of the world - the overseas Chinese, the Armenians, the Greeks (who are partly descended from Phanariots, hence all those shipping magnates) do not show the lopsided Jewish IQ profile where verbal intelligence far outscores the visio-spatial kind. They are not hugely overrepresented in the legal profession like Jews are, or among artists' and athletes' agents who have to draw up and understand complicated contracts.
Most Jewish contributions to STEM were in theory. There were no Jewish Edisons, Teslas, Wright Brothers, Korolyovs or Wozniaks. Tinkering with three-dimensional objects isn't very Jewish. I remember reading an interview with Einstein in which he was asked how his typical work day looked. He said that he stared at a blank piece of paper and thought. Sometimes he took a book from a bookcase, read from it, put it back, thought some more. Sometimes he wrote something down. THAT's Jewish.
Well, the contributions to STEM made by other mercantile minorities aren't concentrated in theory. Actually it's my impression that the children of overseas Chinese are drawn to engineering instead.
The best argument for the occupational theory is that the intelligence of Sephardic Jews seems to have decreased after their expulsion from Iberia to North Africa. High intelligence has costs - genetic diseases and probably other stuff too. Extra neurons require extra resources. Predators have exactly the size of teeth that they need - in the long run nature does not waste anything. Mammal species that come to live in the darkness gradually lose sight. Bird species that don't need to fly anymore gradually lose the ability to do it.
North Africans are less intelligent than Spaniards and Portuguese. Outsmarting them in business transactions is easier than outsmarting Europeans. So perhaps the intellectual capacity that was no longer needed gradually fell away.
A rival explanation of the intellectual decline of Sephardic Jews is that North Africans are more clannish than Iberians. I don't know if it's a good idea to fight fire with fire, but the best way to oppose clannishness is definitely with clannishness. It's certainly a better weapon for that purpose than intelligence. One might call this the it-takes-one-to-know-one theory of interethnic relations. The more clannish behavior of North Africans could have reduced the Sephardim's business opportunities. As they became less of a mercantile minority, their need for high intelligence would have decreased, and, as I said before, in the long run nature does not waste resources.
Both of the explanations for the intellectual decline of Sephardic Jews that I'm aware of imply that the occupational, mercantile theory of Jewish intelligence is correct. But Jews' high verbal intelligence compared with other mercantile peoples implies that the Talmudic theory is correct. Of course both could be correct. Several causes could have contributed to the observed outcome.
The third, Levantine theory of Jewish intelligence starts with the fact that the main mercantile minority of the 1200 BC - 200 BC period in the Mediterranean were Phoenicians. They were close cousins and neighbors of ancient Israelites. From what I understand, the two languages were mutually intelligible in Old Testament times. "Phoenicians" is a Greek term. They actually called themselves Canaanites. Israelites started off as a subset of Canaanites, the hicks from Canaan's southern uplands, but then developed unusual religious theories of their own and split off into an endogamous community. The remaining Canaanites, the people of what's now coastal Lebanon, were both more cosmopolitan and more culturally conservative than the Israelites. Which is unusual. They kept the ancestral Semitic polytheistic religion and the ancestral demonym "Canaan" much longer than the Jews.
Jews did not display many outward signs of high IQ until the appearance of Radhanites in the second half of the first millennium AD. Yet their close cousins Phoenicians dominated Mediterranean commerce 2,000 years before that. Could that be a coincidence? Phoenicians' closest living descendants, Levantine Christians, are pretty good at business. Everyone who follows Steve Sailer's blog is aware of Carlos Slim and Tony Rezko, but more importantly than that the Christian community of Lebanon is much wealthier than local Muslim communities. Levantine Christian immigrants to the West assimilate very quickly. They and car-be-queing Algerians of the French banlieues might as well come from different planets.
I've once seen someone suggest that modern Jews descend from Phoenicians more than from ancient Israelites. He thought that the Phoenician mercantile diaspora could have converted to Judaism en masse during the centuries right before or right after the start of the Christian era. Why? Because monotheism usually trumps polytheism and because the particular Jewish kind of monotheism drew on Canaanite folklore and was expressed in a language that Phoenicians and Carthaginians understood.
I'm not aware of any evidence that this actually happened, but it would certainly explain some things. Fortunately modern genetic techniques have made this hypothesis testable.
I think that the first two theories, the occupational and the Talmudic, could probably explain Jewish intelligence together. It's possible that Jews also inherited some amount of business acumen from ancient (I'm talking about 2nd millenium BC) Canaanites. The idea of the Phoenician diaspora converting to Judaism in Roman times is a lot of fun, but I think it's a bit too crazy to be true.