Neither writer troubles himself to say what he means by volatility. When used by sombre-sounding financial news reporters, it tends to mean security prices going down a lot (prices going up a lot are just as volatile, but they don't evoke the same atmosphere of impending doom). But as a term of art in finance, it means the standard deviation of the logarithm of price returns, scaled by the square root of the time interval over which each return occurs - Black and Scholes' seminal 1973 paper on option pricing uses the concept, describing it as the square root of the "variance rate".
In a simple model, security prices follow a geometric Brownian motion. In this model, the observed volatility is expected to be same whatever time interval of returns is used. This model is far from being an exact description of the real world - much published work on option theory is concerned with its flaws - but it is a useful approximation. Under this model, what would be the effect on volatility of an FTT? Assuming that trades become less frequent, but otherwise occur at the same prices, it would make no difference. (The result is essentially the same if one introduces an additional drift to compensate investors for reduced liquidity.)
One minor flaw with the model is that if trading occurs at high frequency, prices may bounce between the bid and the offer, introducing additional volatility if the return periods used to observe it are very short. An FTT would largely eliminate this effect. But the effect does no one any harm, apart perhaps from causing some inconvenience to anyone engage in high-frequency analysis of market-price data. Could this be what Richard Murphy means when he says less liquidity very obviously gives much less volatility? I don't think so, I think he just means that traded prices don't move when no trades occur. Which is true, but not to anyone's advantage.
There are other high-frequency noise effects which have been theoretically analysed. The conclusion tends to be that some reduction in short-term volatility is possible, at least in theory, if some sorts of high-frequency trading can selectively be discouraged. (More on this below.)
A more important flaw in the model is that in practice there are far more large price moves than it predicts, unless one allows very large process volatilities to prevail temporarily. This effect can be modelled by introducing a jump diffusion term to the price process. Although these large price moves may not be related to an underlying volatility process, they nevertheless contribute substantially to observed volatility whenever they occur. So if the incidence of these large moves could be reduced, there could be a substantial reduction in volatility, of precisely the sort one would wish to see if concerned about market price instability.
Some large moves may be caused by speculative activity. Holders of securities may be induced, or even compelled, to sell them if the price falls far enough. For example, as I noted in another post, when sovereign debt yields get large enough margin requirements are made more onerous, making it still more unattractive to hold the bonds and leading to further selling. This can give two distinct possible prices for the same instrument. Speculators may be able to gain by pushing the price from one possible value to the other one. An FTT would inhibit such speculation. So there is at least a mechanism by which it could reduce volatility. Whether this is significant could be determined only empirically.
Which brings us to Worstall's commentary. Whereas his introductory article is emphatic that an FTT would increase volatility, his actual report is more measured: it quotes this from a report by the Institute of Development Studies at the University of Sussex:
The balance of evidence suggests that there is a positive relationship between transaction costs and volatility, although the size of this effect varies across different studies. Whether a Tobin Tax would affect volatility in the same way as underlying market transaction costs is not clear.and concludes that "this suggests that a transaction tax would increase, not decrease volatility." But the quotation seems to have been carefully selected to suit Worstall's position. The discussion on volatility is much longer and more nuanced. Ideally you should read the whole thing, but I'll offer a flavour of it by quoting the whole of the paragraph Worstall quotes from:
Nonetheless, the overall conclusion from the empirical evidence is more one sided than the theoretical work. The balance of evidence suggests that there is a positive relationship between transaction costs and volatility, although the size of this effect varies across different studies. Whether a Tobin Tax would affect volatility in the same way as underlying market transaction costs is not clear. The Swedish experience of imposing a tax on equity transactions may have increased volatility, but the size of the tax was large; there is no evidence that UK Stamp Duty had any effect on volatility, although it clearly affected returns on equity.My summary is that the theoretical work tends to support the case that an FTT can reduce short-term volatility. The empirical work suggests the opposite, but does not of course rule out the possibility that a carefully designed FTT could work as suggested by the theory. But none of this matters very much because short-term volatility doesn't matter very much.
Importantly for my argument about jumps, the report notes that:
Unfortunately, to our knowledge, there are no papers which look at the impact of FTTs on the probability of a crash or adjustment taking place...We see this as a major gap in the literature.To answer my original question, both Murphy and Worstall are wrong. Murphy is completely wrong, except perhaps under some definition of volatility known only to himself. Worstall is wrong in stating a definite answer to the question not supported by the evidence he cites. The true answer is that we should not expect any great effect on short-term volatility, but that any small effect is somewhat more likely to be up than down. And that there is no way of knowing whether they would be a useful reduction in the risk of the occasional large moves that we really care about when we worry about volatility.