How technology will help economists to do better predictions? Would technologies as AI, BI and Big Data help the economists to make better predictions and test models to solve problems like "What level of fiscal stimulus is better for a especific country?"

Is it something for the future or its already been used?
I'm an economist by training who also is a programmer and works with a lot of data scientists, so I've some insight into this area.  One of my projects at the Urban Institute is trying to bridge the gap between these fields, and part of our work, supported by the Sloan Foundation, is publicly available here.

To some degree the answer is yes, but there are huge obstacles as well.  Some are surmountable with work, like differences in terminology, programming platforms (knowledge of SAS or Stata versus R or Python) and conventions (do others in your field understand and/or accept the results of machine learning models?).  Others are much more difficult to surmount, such as the size of data available.

Essentially, the fields that make extensive use of AI and machine learning have huge amounts of data.  They can afford to, say, set aside a million observations for training the model and then test the model on the other nine million.  Economists, and social scientists in general, however, are often lucky if they have 100 observations.  Many macroeconomic variables are annual, or quarterly.  Some are monthly, which means if you can get 30 years of observations then you've got 360 time periods!  Data-rich by social science standards, but not even a rounding error in many data science models.

That said, computing power and sophisticated data collection are making it more and more feasible to approach social science questions with big data.  Social media is a major area that social scientists are just beginning to reach into.  However, some areas of economics will likely remain closed off to data science methods due to the nature of the data.  Your fiscal stimulus example might very well be one - the relevant data just isn't produced that fast.

So the answer to your question is yes, with reservations and a hope for the future.