How prevalent is the use of machine learning among economists? I wonder how machine learning, particularly deep neural net which is considered the state-of-the-art among many data scientists, is used among economists, or other experts who is in in the similar field to predict economic situations, such as bank analysts, etc...

I know in econometrics people heavily use statistics. But it is focused on  statistics, not on machine learning, let alone deep learning.

How prevalent is it? What kind of methods/algorithms/models, if any, are frequently used for what kind of purposes among what kind of economists? Where can I see their work (e.g. blog, paper, etc...)
I will attempt to answer the first (How prevalent is it?) and last question (Where can I see their work?).

There was a recent post in The Economist about the emergence of machine learning into standard economic papers. They produced a nice graph, reproduced below:



Albeit machine learning is confounded with big data, it shows a rise in their use since 2014. Surely, this is a very narrow selection of the literature (NBER working papers, and only abstracts), but is a start. 

Regarding where you can find papers using machine learning, you can use "keyword" search here (26,665 documents are found), or here (337 documents are found). The latter allows you to select dates, which you could use to build your own indicator of machine learning related publications per year.

Finally, related to blogs, I am not aware of a dedicated ML/DL economist's blog. However, here there is a very useful blog aggregator, which has indexed most of the "serious" blogs available. The full list of blog posts indexed is here. A search for "machine" or "deep" does not yield a result. However, there are some hits for "econometric" and "statistics" which might help you.