For numbers 1 and 2, see this post.
Number 3. We must reduce the size of the state.
This argument is often there but unstated, because to say it explicitly involves a deception. Instead it sometimes goes by the euphemism of ‘structural’ or ‘supply side’ reform. (No, I’m not saying there are no genuinely useful structural reforms out there, but just what some people mean when they use this term.) But as those making the case for austerity get more desperate, I have seen this argument a few times recently.
It involves a deception, because reducing the size of the state has nothing in principle to do with austerity and stimulus. I personally have no strong views about what the size of the state should be: some things are clearly done better by the private sector, while others are done better by the state, and how this eventually pans out for the aggregate I have no idea. But this has almost nothing to do with the need to increase demand when interest rates are at the zero lower bound. The deception comes when austerity mainly involves cutting spending (as in the UK), because it is anticipated that it will be very easy to cut taxes later on once austerity is over.
When I say it has almost nothing to do with stimulating demand, this is why I say almost. A long established and theoretically robust method of stimulating demand is a balanced budget fiscal expansion, where you temporarily increase government spending by temporarily raising taxes. However as it need involve nothing more than bringing investment projects forward in time (e.g. repairing roads and schools before they completely fall apart), it is not really increasing the size of the state. The idea that what is temporary is bound to become permanent does not stand up.
4. We must think of the children
This is annoying not because it is wrong in principle. Instead it is wrong because it either ignores who suffers the costs of austerity, or because it is not genuine. The argument that is right in principle is that, by increasing debt, we are ceteris paribus redistributing money from future generations to the current generation. There may be a complete offset if that increase in debt avoids hysteresis effects (or enables investment with beneficial supply side effects). Yet even leaving that aside, there are often very good reasons to redistribute income. When a country suffers a natural disaster, both governments and individuals freely give money to help those involved. We can think about the recession as a similar disaster.
If that does not convince you, ask who is bearing the brunt of this recession. All around the world, youth unemployment has risen by more than unemployment in general. If you asked those who cannot find a job after leaving school or college whether they would be willing to pay higher future taxes in order to get a job today, what do you think their answer would be?
Why do I suspect that this argument is sometimes not genuine? Because some of those who make this case also argue against measures to tackle climate change. Now even if you are sceptical about the science, the potential costs of you being wrong and 98% of scientists being right are so great that if you really cared about future generations you would support measures to reduce carbon emissions. (See Martin Wolf here or Martin Weitzman here.) So when, for example, a recent Wall Street Journal article argued that “we need an exclusive focus on supply-side reform [reducing the size of the state] to promote growth. Luxuries such as family-friendly employment legislation or green initiatives such as the carbon taxes are no longer affordable in the age of austerity” you know something is not right. The biggest risk to the well being of future generations right now is climate change, so what is the point of increasing future growth if the cost is doing nothing to reduce that risk. Of course that combination might make sense if you only care about what happens in the next few decades, but if that is your view then don’t tell me we should avoid a short run increase in debt for the sake of future generations.