How was the big stick policy extended by dollar diplomacy?

The "big stick diplomacy" describes Roosevelt's foreign policy, which basically excercises kindness but with reasonable foresight into potential issues. The "dollar diplomacy" refers to the way in which the dollar is used in foreign policies to manipulate key issues mainly taking control of the Panama Canal. Dollar diplomacy effectively extended the reach of the US governments foreign endeavours by instigating control over key areas of financial revenue; it has been considered a failure mostly, due to the effect it has had upon Latin American communities, where uprisings and resistance to foreign governments rendered many of these projects null. 

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

producing or giving rise torelating to or engaged in the production of goods, crops, or other commodities.

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.