options, where volatility would probably increase with reduced volumes. Behavioral finance theoretical models, such as those developed by Wei and Kim (1997) or Westerhoff and Dieci (2006) suggest that transaction taxes can reduce volatility, at least in the foreign exchange market. In contrast, some papers find a positive effect of a transaction tax on market volatility. Lanne and Vesala (2006) argue that a transaction tax "is likely to amplify, not dampen, volatility in foreign exchange markets", because such tax penalises informed market participants disproportionately more than uninformed ones, leading to volatility increases. Empirical studies In most of the available empirical studies however, no statistically significant causal link has been found between an increase in transaction costs (transaction taxes or government-controlled minimum brokerage commissions) and a reduction in volatility—in fact a frequent unintended consequence observed by 'early adopters' after the imposition of a financial transactions tax (see Werner, 2003) has been an increase in the volatility of stock market returns, usually coinciding with significant declines in liquidity (market volume) and thus in taxable revenue (Umlauf, 1993). For a recent evidence to the contrary, see, e.g., Liu and Zhu (2009), which may be affected by selection bias given that their Japanese sample is subsumed by a research conducted in 14 Asian countries by Hu (1998), showing that "an increase in tax rate reduces the stock price but has no significant effect on market volatility". As Liu and Zhu (2009) point out, [...] the different experience in Japan highlights the comment made by Umlauf (1993) that it is hazardous to generalize limited evidence when debating important policy issues such as the STT [securities transaction tax] and brokerage commissions." Is there an optimum Tobin tax rate? When James Tobin was interviewed by Der Spiegel in 2001, the tax rate he suggested was 0.5%. His use of the phrase "let's say" ("sagen wir") indicated that he was not, at that point, in an interview setting, trying to be precise. Others have tried to be more precise or practical in their search for the Tobin tax rate. According to Garber (1996), competitive pressure on transaction costs (spreads) in currency markets has reduced these costs to fractions of a basis point. For example, the EUR.USD currency pair trades with spreads as tight as 1/10 of a basis point, i.e. with just a 0.00001 difference between the bid and offer price, so "a tax on transactions in foreign