Climate change research and policy
Climate change is a complicated subject which is difficult to predict with accuracy.   The IPCC's predictions at least since their 3rd report (TAR) appear to be quite good, but good over the first few years or decade and a half vs good for predictions up to 2100 remains inexact and perhaps unclear.

Governments (many not all) do rely in the scientific research of the IPCC both to anticipate coming changes and determine action, but these are difficult questions, as a global effort is required to reduce the greenhouse gas footprint, and individual nations can only control their own policies.   Even if we know, 100%, the future effects of climate change, it would still be a difficult transition away from fossil fuels towards a more climate neutral approach because (If I may borrow the word from Al Gore), fossil fuels are convenient.   They're relatively easy, especially for nations that don't need to import them and they're economically viable. 

That's a general outline.   The scientific predictions are important because without them, government leaders would be making policy decisions blind (as opposed to making them based on imperfect projections), and imperfect is better than blind.  

There are similar predictions/estimates made across the gamut in political policy decisions.  Estimates are made on future costs of government programs and on tax policies and national debt, or trade.   We're always trying to make mathematical or scientific estimates which, in theory, help leaders make predictions for the future.

Ofcourse, sometimes, you get leaders who don't care, who don't listen to the forecasts, climate change or economic indicators.  Politics is a messy game.


  Are there any statistics which help to visualise the effectiveness of
  new scientific findings or new technology innovation inducing a change
  in government policy to help kerb climate change?


I don't know where you'd find such statistics and I've never seen any.    Statistics can be a tricky business with a long game approach like this one.   There's a lot of factors.