I unfortunately don't have enough time to give as thorough an answer as I like, but the decline focuses on two factors. The first is the decline end of the policy of imperial preference. From the late 19th century onwards, the British followed a policy of encouraging trade within the empire through a policy of quotas and lower tariffs. This policy was especially strong during the great depression. Trade preferences meant that something like three quarters of New Zealand's trade were oriented towards the UK, and New Zealand became highly dependent upon exports of wool.The period of the World Wars and Korean wars created massive demands for woollen cloth. New Zealand's prosperity during this period was based in part on the high price (guaranteed at set prices by the UK rather than the market) of wool, and the fact that New Zealand had a stranglehold on the UK market.

However, free tariffs started dropping dramatically in the post-WWII period as free trade was seen as vital and the protectionism of the Great Depression seen as a mistake. While New Zealand kept many of it's privilges, tariffs on American, European, etc wool created competition. The UKs joining the European Community in 1973 was the final end of New Zealand's privileged position, as the EC demanded non-EC countries should not get any special trade privileges, and New Zealand lost it's previous privileged status. At the same time, agricultural exports liberalized to a much lesser extent than other commodities, so New Zealand found itself in a very difficult trade position,.

A second series of problems came from the fact that New Zealand had one of the more controlled economies in during the post-war period. New Zealand was one of the only developed countries that did not liberalize the current account and had a highly restricted regime for importing goods. The government tried to make major investments in state owned steel works, chemical plants etc after the discovery of natural gas. However, most of these investments proved to be unprofitable. At the same time, poor macroeconomic management led to high and persistent rates of inflation, and current account deficits.

From 1984 onwards, New Zealand engaged in one of the most extensive liberalizations under Roger Douglass, and New Zealand underwent one of the largest liberalizations in the world. The World Bank currently ranks New Zealand 1 in ease of doing business, and New Zealand is consistently at the top of rankings of how "Free Market" economies are. Moreover, New Zealand has succesfully diversified it's agricultural base. It produces massive amounts of whine, fresh fruit for temperate climates and above all milk for China. The combination has allowed New Zealand to have steady growth since the 1980s, and New Zealand's per capita income has grown steadily since that period.

Taking 1950 as the starting point is misleading because that year New Zealand experienced a windfall the likes of which few countries have been blessed/cursed with. Back then less than two million people lived in New Zealand but they had 35 million sheep. The amount of sheep made New Zealand the world's third largest wool producer and almost all that wool was exported.

Because of the Korean War the United States had decided to replenish its strategic commodity stocks, including stocks of wool. This caused the average price of wool to more than double in the international markets (and tripling for the grade of wool the US military wanted). So low population combined with an enormous increase in the value of their primary export commodity resulted in a major increase in GNP. For the year ending 31st march (back then NZ stats didn't follow the calendar year) GNP in 1949 was 480.7 NZ£, in 1950 it was 549.1 NZ£ and in 1951 it was 658.8 NZ£. In other words GNP increased by almost 40% during this period. Just like that New Zealand had the world's 3rd highest per capita income (note that there were far fewer independent countries in the world back then).

Then the stockpiling ended and wool prices and NZ GNP returned to normal. Many an unwary economist who chose 1950 as a convenient starting point and who didn't know about the "Wool Boom" have had their international comparisons polluted by this single data point (most famously Reinhart-Rogoff).