How to test exception raising in Rails/RSpec?

Use expect{} instead of expect().

Example:

it do 
  expect { response }.to raise_error(Errors::CarBrandNotFound)
end

In order to spec error handling, your expectations need to be set on a block; evaluating an object cannot raise an error.

So you want to do something like this:

expect {
  get :index, car_brand_id: 0
}.to raise_error(Errors::CarBrandNotFound)

See Expect error for details.

I am a bit surprised that you don't get any exception bubbling up to your spec results, though.

get :index will never raise an exception - it will rather set response to be an 500 error some way as a real server would do.

Instead try:

it 'raises CarBrandNotFound exception' do
  controller.params[:car_brand_id] = 0
  expect{ controller.car_brand }.to raise_error(Errors::CarBrandNotFound)
end