In a recent post I showed why that can't be true. The European economies began to advance by at least the year 1100 AD, long before any colonial contact with Asia or Africa. And there was a big jump in economic growth in about the year 1800 AD, which coincides with the beginning of the Industrial Revolution - which means that it was the innovations in industrial organisation and technique in England and elsewhere which powered the sudden leap in Western economies.
A reader, Chris, sent in a link which provides more evidence that white colonisation does not explain economic inequality. Two American economists, William Easterly and Ross Levine, have undertaken research to discover the economic impact of white colonisation on the long-term prosperity of a country.
What they discovered was that white colonisation predicts improvements in long-term prosperity rather than poverty. In other words, the more whites living in a country in 1700, the higher the GDP of a nation in the year 2000. Whites brought relative prosperity, not poverty.
From the summary:
We find a remarkably strong impact of colonial European settlement on development. According to one illustrative exercise, 47 percent of average global development levels today are attributable to Europeans. One of our most surprising findings is the positive effect of even a small minority European population during the colonial period on per capita income today, contradicting traditional and recent views.
That 47 percent statistic is explained further here:
Using the 2000 population weights, the data and estimated coefficients indicate that 47% of the development outside of Europe is attributed to the share of European settlers during the early stages of colonization ... it is striking how much of global development is associated with Europeans (not even considering the development of Europe itself).
What the statistic means is that if, say, an African country has managed to increase its GDP by $1000 per capita over the period 1700 to 2000, then $470 of that improvement can be attributed to the presence of whites in the year 1700. If there had been no whites active in that African country, then that $470 GDP per capita improvement would not exist.
The researchers found that you could predict economic improvements by the number of whites in a particular country in the early stages of colonisation. They give this example for Brazil:
...consider just a one percentage point increase in Euro share in the case of Brazil. The estimated coefficients suggest that if Brazil had a Euro share of 0.084 rather than 0.074, then its average GDP per capita over the period from 1995 to 2005 would have been $9,798 instead of $7,942.
I am not quoting these figures in order to try to prove that everything about colonisation was positive for the countries affected. But they do provide strong evidence against the claim that the Western nations got rich at the expense of other nations. Nations which were left alone by the Western colonial powers are worse off today in economic terms, not better off.