So does that mean the the convergence would continue without the world wars?
It's hard to say, since 1890s, the U.S. economy was growing at a faster rate than most European countries, the exceptions being Italy, Norway and Finland. However, this was a result of the industrialisation of the U.S. along with its growing frontier. Keep in mind that Argentina and Canada had faster rates of growth during this period as their economies were even more underdeveloped during this period.
I imagine that the U.S. would continue to grow at a faster rate at least for a while. What is more important is that without the wars, the divergence wouldn't be so sharp, particularly by 1950. During the 19th century economic growth was generally lower without the booms and busts that would occur after abandonment of the gold standard. When economic contractions occurred, they were usually sharp, such as in 1908 when U.S. GDP declined by 8.2%, however recoveries were also quicker, as in 1909 when the GDP grew by 12.3%.
One important thing that the first World War altered was it made New York a centre of global finance and banking. Prior to the war, London and Paris were by far home to the world's largest banks and insurance companies. This allowed the two to become the world's largest creditors with $20 billion of British capital invested abroad. France had just under half of that at $9.7 billion and German was third with $5.8 billion. Berlin was the world's third largest centre of banking based on deposits, whilst New York was close on its tail in fourth place. However, Vienna this was followed by Vienna in fifth place, and it can be said that in banking at least, finance was slow to catch up to a country's decline as a great power. The outflow of capital to the U.S. during World War I and later World War II drastically altered this and as a result, Berlin lost its position as did Paris and Vienna, however London still vies with New York as the world's largest financial centre.
Trade and Commerce
Britain remained the world's largest trading nation in 1913, and 37% of its trade was with its empire, the bulk being with the Dominions and India (31%). However, Britain slipped behind Germany and the United States in terms of GDP. British industrial exports were also less sophisticated than those of Germany with coal rising in value and accounting for 9% of British exports in 1910. Another 14% were textiles, whereas Germany and the United States were leading in the production and export of electronic equipment and chemicals. The dominions provided a safe market, but by 1913, the U.S. had replaced Britain as Canada's leading source of goods (though Britain remained Canada's largest market).
By World War I, Germany had emerged as the world's second largest exporter, exporting $2.4 billion worth of goods to other countries.
Unlike Britain, Germany traded overwhelmingly with neighbouring countries, it's noteworthy that by 1913, Germany was by far Russia's leading trading parter, providing nearly two-thirds of its imports. Interestingly enough, Germany was displacing France in much of Latin America as the second largest supplier of goods. However, 76% of all German exports went to Europe, 15% to America, 5% to Asia and the rest to Africa and Australia, a mere 0.5% went to the colonies. As for imports 58% came from Europe, 29% from America, 10% from Asia, and 0.5% from the colonial empire. As for Germany's colonies, they provided a mere 0.5% of Germany's raw materials.
The United States emerged as the world's largest economy by 1913, and it was making inroads in world trade. It dominated trade with Canada, Mexico, Central America, the Caribbean and Northern Latin America along with its territories in the Philippines and Liberia. It also displaced Britain, as Germany's largest source of imports before the war, and was among the top 5 trading partners for most European nations.
France like Britain was in a malaise, as it had been Europe's largest economy a century earlier. Though still an important country, France's trade was overwhelmingly with Europe and a mere 8% with its empire. However, France (along with Belgium) did continue to be a major supplier of foreign capital in Russia, Latin America and China. However, France did dominate the luxury goods sector at the time, exporting fine silks, luxury automobiles, furniture and porcelain.
Below is a comparison of the share of imports from selected nations in 1913.
British Imports as a % of imports with rank
India 64% (#1)
Australia 61% (#1)
South Africa 58% (#1)
Argentina 31% (#1)
Chile 30% (#1)
Egypt 30% (#1)
Ceylon 28% (#1)
British East Africa 27% (#1)
Uruguay 27% (#1)
El Salvador 26% (#2)
Norway 26% (#2)
Portugal 26% (#1)
Sweden 25% (#1)
Brazil 24% (#1)
Greece 24% (#1)
Peru 23% (#1)
Ottoman Empire 22% (#1)
Venezuela 22% (#2)
Canada 21% (#2)
Colombia 20% (#2)
Nicaragua 20% (#2)
Bolivia 18% (#2)
Spain 18% (#1)
China 17% (#3)
Denmark 17% (#2)
Japan 17% (#2)
Russia 17% (#2)
Belgian Congo 16% (#2)
Guatemala 16% (#3)
Bulgaria 15% (#3)
Costa Rica 15% (#3)
Persia 15% (#2)
France 13% (#1)
Honduras 13% (#2)
Cuba 11% (#2)
Malaya 11% (#2)
Netherlands 10% (#4)
German Exports
Kamerun 79% (#1)
Russia 64% (#1)
Finland 44% (#1)
Austria-Hungary 40% (#1)
Denmark 38% (#1)
Sweden 35% (#1)
Switzerland 34% (#1)
Bolivia 33% (#1)
Norway 30% (#1)
Romania 30% (#1)
Netherlands 27% (#1)
Chile 25% (#2)
Bulgaria 22% (#2)
Guatemala 20% (#2)
Dominican Republic 18% (#2)
Argentina 17%(#2)
Brazil 17% (#2)
Italy 17% (#1)
Uruguay 17% (#2)
Peru 16% (#3)
Portugal 16% (#2)
Colombia 15% (#4)
Costa Rica 15% (#2)
United States 15% (#1)
France 13% (#2)
Mexico 13% (#2)
Belgium 12% (#2)
Belgian Congo 11% (#3)
Honduras 11% (#4)
United Kingdom 10% (#2)
United States 10% (#2)
French Exports
Switzerland 20% (#2)
Spain 16% (#2)
Belgium 15% (#1)
Colombia 15% (#3)
Honduras 11% (#3)
Brazil 10% (#4)
Haiti 10% (#2)
Argentina 9% (#4)
Egypt 9% (#3)
Italian Exports
Switzerland 10% (#3)
American Exports
Puerto Rico 84% (#1)
Hawaii 81% (#1)
Haiti 73% (#1)
Honduras 67% (#1)
Canada 65% (#1)
Dominican Republic 62% (#1)
Nicaragua 56% (#1)
Cuba 52% (#1)
Costa Rica 51% (#1)
Guatemala 50% (#1)
Mexico 50% (#1)
El Salvador 40% (#1)
Venezuela 33% (#1)
Colombia 27% (#1)
Serbia 25% (#2)
Peru 21% (#2)
UK 18% (#1)
Chile 17% (#3)
Japan 17% (#3)
Brazil 16% (#3)
Germany 16% (#1)
Argentina 15% (#3)
Italy 14% (#2)
Australia 12% (#2)
Austria-Hungary 10% (#2)
France 10% (#3)
Netherlands 10% (#3)
Austria-Hungary Export Markets
Serbia 42% (#1) (1911)
Bulgaria 32% (#1)
Romania 22% (#2)
Greece 16% (#3)
Ottoman Empire 15% (#2)
Japanese Export Markets
Korea 61% (#1)
China 21% (#2)
Hawaii 8% (#2)
Russian Export Markets
Persia 57% (#1)
Finland 31% (#2)
Greece 20% (#2)
Germany 13% (#3)