RICH countries tend to produce more scientific, cultural and technological innovation than poor ones do. Wealth is most often created in countries with stable institutions and a firm rule of law. It can be used to fund research-and-development, and to build human capital through public education and health care. However, a new ranking of innovation in 126 countries highlights a striking exception to this trend: oil-rich Arab states states are far less innovative than their prosperity would suggest.

Countries like Kuwait, Qatar and the United Arab Emirates enjoy many of the advantages that generally lead to innovation. All three are rich—mostly thanks to their oil and gas resources—and enjoy levels of GDP per head higher than America’s. They have also made large investments in domestic infrastructure, facilitating the exchange of goods and ideas within their borders. Nonetheless, they rank between 38th and 60th in this year’s edition of the Global Innovation Index, an annual study published by Cornell University, INSEAD business school and the World Intellectual Property Organisation.

The Index is constructed from a variety of economic statistics and societal factors, such as government spending on education, access to communications technology, political stability, ease of starting a business and patent generation, among others. The three Arab countries lag far behind comparably wealthy countries on measures of the strength of government institutions, human capital, business sophistication and modern technological output.

Poorer Arab economies display a similar pattern of underperformance. If we use each country’s GDP alone to predict their scores on four sub-indices that make up part of the larger innovation index, the differences from predicted values are striking across the region. The average Arab country scores about 25% lower than predicted in the “institutions” (mainly government and business) category, 22% lower for investment in human capital, 36% lower for knowledge and technology outputs, and 38% lower for business sophistication.

Arab petro-states may enjoy Western levels of consumption but lack Western levels of productivity. Their poor showing in the index is one indication of the mountain they have to climb to find non-oil sources of growth. Under their “rentier” system, ruling families extract rents from oil and gas exports, and distribute the revenues in the form of easy government jobs (mostly for men) and generous benefits, not least subsidised fuel, electricity and water. Some rulers realise that, given high rates of population growth, their model is unsustainable. Saudi Arabia’s social reforms—including the decision earlier this month to let women drive cars—are part of an attempt to modernise the economy (see video). But weaning Gulf states off oil will be hard (see special report on the Gulf).