Oh shit, didn't notice you had replied
The bold part is only true if people stash their savings under the mattress. Otherwise increased savings results in more capital accumulation and therefore higher GDP, unless the economy is dynamically inefficient, which is only a theoretical possibility and has never happened in the real world. The relationship between income and saving is much more complicated than that. Check out the permanent income hypothesis for reference. I didn't really read your reference because its not a peer reviewed publication, so it has no merit in a scientific debate.
It does increase the saved financial capital, theoretically making it cheaper to invest, but usually a lack of saved funds is not the problem in a developed economy at least, not with fractional lending. The Permanent Income Hypothesis also does fill the gap between the Keynesian theory and the empirical evidence, but it doesn't hold true for the entirety of income over the entirety of people. In effect, it's similar to what I said about taking the VAT for people's whole lives (it has a lot to with that after all), the effect is reduced but still exists.
Concerning my source, you are right, it's no real scientific paper. What I was posting it for wasn't the analysis though, but merely the data, which I suppose still holds a risk of being false, though I wouldn't expect it. And yes, it is just a correlation, but that's the only thing I wanted to show - people with higher incomes save proportionally more. They do make up for it with using some of the accumulated savings later in life, as the permanent income hypothesis predicts, but this doesn't account for everything.
For high marginal rate the drawback is not slight at all. As to the accumulation of capital in a small portion of society, I have no idea what you base this on. Capital gains and corporate taxes are of course even worse than income taxes, extremely inefficient as they directly disincentive investing.
A lack of these taxes result in a higher degree of inequality, and that very much so. This in turn damages the economy, and worse, the general living standard, far more than the relatively small disincentive these taxes would result in.
The only way to raise money without any distortions is a lump sum tax, which is obviously very regressive and unpopular and impossible to implement. The next best thing in terms of efficiency is VAT + other consumption taxes because they promote saving and some pigouvian taxes which are paretto improving anyway. There was a proposal in the USA, called the fair tax or something like that, to replace all taxes with a federal VAT. It didn't pass but it was a very good idea. On top of all the other benefits it simplifies the administration a lot (which is good economically but bad politically because redundant civil servants vote for the opposition). I don't see why a tax policy that raises the same amount of money would lead to worse public services. By the way, a very small percentage of the revenue goes to public services, most of it goes to benefits and redistribution of some sort. The public services, most of which should be private anyway, is just a smokescreen by the politicians.
The vast majority of government spending, in general of developed countries, goes to three sectors: Pensions, Education & Health. There might be a lot of spending in defense as well, depending on the country. Classical redistributions, unemployment benefits and the likes, make up relatively little of total spending, not more than 10%
The US for example:
Or in all it's detailed glory:
https://www.whitehouse.gov/sites/default/files/omb/budget/fy2016/assets/tables.pdf
Of course, pension are a also a form of redistribution. However, it is by far the best form of financially security for the elderly, private pension funds lack security (as seen 2001 & 2008, and when it comes to pensions, security is far more important than possible greater benifits) and has far higher administrative costs.
And not to open up another huge topic, but privatization of public services usually leads to stark reduction of quality and/or coverage in that sector. They are merit goods after all, pure market mechansims by themselves won't provide them adequately. Health care, education, water, even railways have in most cases deteriorated immensely after their privatization. You can make a case in favor of privatization in the case of industries though, generally speaking.
The only real upside of a lump sum tax is simply the removal of costs in the ministry of finance.
That is true but also means that a progressive income tax is not that effective in reducing inequality.
On it's own, no, that's why I've already stressed the importance of taxes on capital or capital gain.