### Discussion Paper

## Abstract

This heterogeneous interacting agents model of a financial market is a generalization of the model proposed by Westerhoff (The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies) by traders who are allowed to have different investment horizons as introduced by Demary (Who Does a Currency Transaction Tax Harm More: Short-term Speculators or Long-term Investors?). Our research goals are, first, to study what consequences the introduction of heterogeneous investment horizons has for agent-based financial market models and second, how effective transaction taxes are in stabilizing financial markets. In detail, we are interested in how the popularity of different trading rules and investment horizons change due to taxation and how emergent properties from the interaction of traders like bubbles and crashes, excess volatility, excess kurtosis and volatility clustering change. Numerical simulations reveal that under taxation traders abstain from short-term trading in favour of longer investment horizons. This change in behavior leads to less excess volatility and diminishing volatility clusters for small tax rates. When the tax rate exceeds a certain threshold, excess volatility and misalignments increase as also found in Westerhoff (Heterogeneous Traders and the Tobin Tax). The reason is, that the longer term fundamentalist trading rule becomes unpopular in favor of the longer term trend-chasing rule.

Paper submitted to the special issue

Managing Financial Instability in Capitalist Economies

## Comments and Questions

See attached file

Thank you very much for this positive reply. I highly appreciate your helpful comments.

Concerning comment 1:

I agree with the referee that I should elaborate on the introduction and shorten it. Bubbles and crashes emerge in agent-based financial market models from the interaction of heterogeneous traders. Taxing financial ...[more]

... transactions will alter traders decisions which might have an effect on bubbles and crashes. The aim of this paper is to analyze the effectiveness of transaction taxes for reducing speculative bubbles. But I agree with the referee that I should shorten the discussion on speculative bubbles in general in the introduction. As suggested by the referee I will concentrate on empirical evidence on the effects of transaction taxes of financial market volatility instead.

Concerning comment 2:

To my best knowledge, Demary (2008) is the first paper which introduces heterogeneous investment horizons in agent-based financial market models. Survey studies like Taylor and Allen (1992) provide empirical evidence that traders are characterized by heterogeneous investment horizons. They find that short-term oriented traders tend to rely on trends in exchange rates, while longer term oriented traders rely on economic fundamentals. Proponents of transaction taxes argue that taxing foreign currency transactions punishes short-term speculation and favors longer-term investments. Punishing short-term speculation will reduce excess volatility and bring exchange rates closer to their fundamental values. For analyzing this proposition one has to introduce traders with heterogeneous investment horizons into the agent-based model. In my paper I will consider the papers dealing with empirical evidence on heterogeneous investment horizons suggested by the referee.

Concerning comment 3:

This paper introduces the heterogeneous investment horizons of Demary (2008) into the agent-based model of Westerhoff (2008). Westerhoff (2008, p. 197) states that this model of a speculative market may represent a stock, foreign exchange or a commodity market. DeGrauwe and Grimaldi (2004) highlight that their foreign exchange market model can also be interpreted as an asset pricing model with one risky asset and one risk-free asset. I will discuss this point in the paper as suggested by the referee.

References:

Demary, Markus (2008), "Who Does a Currency Transaction Tax Harm More: Short-term Speculators or Long-term Investors", Jahrbücher für Nationalökonomie und Statistik, Vol. 228, 228-250.

DeGrauwe, Paul and Marianna Grimaldi (2004), "A Theory of Bubbles and Crashes", Working Paper, University of Leuwen, 8th of January 2004.

Taylor, Marc and Helen Allen (1992), "The Use of Technical Analysis in the Foreign Exchange Market", Journal of International Money and Finance, Vol. 11, 304-314.

Westerhoff, Frank (2008), "The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies", Jahrbücher für Nationalökonomie und Statistik, Vol. 228, 195-227.

Summary:

Demary uses an agent-based financial market model to explore the effectiveness of transaction taxes. Related models so far found that this device has some potential in stabilizing the dynamics of financial markets. What is interesting about Demary’s approach is that he takes heterogeneous investment horizons of speculators into ...[more]

... account, an important feature which is often neglected in agent-based financial market modelling.

The paper’s key finding is that financial market stability may benefit from transaction taxes, at least as long as the tax rate is not too high. Also the underlying model is interesting. I suggest accepting this paper.

Some minor comments:

(i) Of course, there are several ways how one can introduce heterogeneous investment horizons into agent-based models.

-One alternative specification could be to consider exogenous noise terms in (3) and (4), as is done in (1) and (2).

- Another alternative specification could be to consider in (3) that chartists take exchange rate changes between time steps t and t-N into account.

However, I suggest sticking to the current setting.

(ii) Shouldn’t we have parameters kappa_C and kappa_F in (3) and (4)? Please check.

(iii) For kappa_F = 0.04 in (4) I obtain a “fundamentalist reaction parameter” of 0.71, as reported in Section 4, page 12, line 12. However, I do not get the reported value of 1.04 if I use kappa_C = 0.04 in (3). Maybe I made a mistake but please check numbers/formulas.

(iii) Note also that currently the term beta appears in (1), (3) and (5). In (1) it stands for random shocks and in (5) it denotes the price impact parameter. Please check the notation.

Dear Prof. Westerhoff,

thank you very much for these helpful comments and suggestions.

concerning (i):

I will mention that there are these alternative ways of introducing heterogeneous investment horizons.

concerning (ii):

You are right. In equations (3) and (4) should kappa_c instead of beta and kappa_f instead ...[more]

... of psi appear. I will correct it.

concerning (iii):

You are right, 1.04 is wrong, because (1-kappa_c^3)*kappa_c/(1-kappa_c)=0.042, when kappa_c=0.04 is assumed. Fortunatedly, this typo only appears in this example calculation. Equation (3) is correct, thus, the simulations are still valid (this can be inferred from the computer code, which one can download from this page).

concerning (iv):

I will call the price impact parameter phi in order to avoid confusion.

Best regards,

Markus Demary

See attached file

See attached file

Thank you very much for this reply and the helpful comments.

Concerning comment 1:

In order to account for liquidity issues a change in the bahavioral rules is necessary. Therefore, one has to assume that the traders only trade when profits from trading are higher than transaction costs. Otherwise ...[more]

... the agent should decide not to trade. This effect is already incorporated into the selection process for trading rules, but not in the demand functions. When one additionally assumes that the agent takes transaction costs in their excess demand function into account there should be a larger effect of taxation on liquidity.

Concerning comment 2:

I used the same parameter values as in Westerhoff (2008) (despite of the investment horizon) in order to get comparable results. I will perform a stability analysis with variations of the models parameters for different tax rates for checking how robust these results are.

Concerning comment 3:

Prof. Westerhoff also highlighted this point. I will make use of a clearer notation.

Best regards,

Markus Demary

See attache file

Dear reader of my paper,

thank you for your reply and the helpful suggestions therein.

Reply to comment 1:

Yes, your right, in principle it is a structural stochastic volatility (SSV) model. However, this is only the case when all trading rules are perturbed. Under, ...[more]

... the assumption that longer term traders do not have this random component, SSV vanishes for high tax rates when short-term traders stop trading. When adding perturbations to all trading rules, the model is a pure SSV-model. I will highlight this point in the paper.

Reply to comment 2:

That is a good point. I already added a sensitivity analysis in table 3 in a newer version of this paper (see link below). One can infer there, that the policy recommendations of this model a valid for 20 calibrations of this model (all reported numbers are averages over 50 simulation runs of size 5000).

Reply to comment 3:

The kurtosis reacts very sensitive to outliers (one can interpret these outliers as crashes). Because crashes are less likely events which causes huge damages. So I want to measure if the tax prevents or leads to more crashes. I think that under this consideration a statistic which is sensitive to these outliers make sense.

Reply to comment 4:

One can find results for 20 calibrations in table 3 in the updated version of this paper (see link below). The policy results are preserved here, but calibration to a stock market would also be interesting.

Reply to comment 5:

That is a good point. Because it is an assumption which directly leads to the result that volatility clusters vanish under taxation. This effect may (or may not) be smaller in a setting, where long-term rules were also perturbed. I will highlight this point in the paper.

Reply to comment 6:

See the sensitivity analysis in table 3 in the updated version (link below). When the investment horizon N increases, distortion declines. Thus, long term traders have a destabilizing effect. Therefore, medium term traders, would add an additional destabilizing effect.

Reply to issue 1:

0.01 means 1 percent. This is the case for all variables. When I report percent in the text I scaled the value by 100%. Actually, the time-varying parameter in figure 8 is not normalized to zero. This is just a typo by copy-and-past from figure 1.

Reply to issue 2:

The difference between the price collaps in period t=500 and t=1500 lies in the fact that in t=500 the number of short-term chartist is 100% for less trading days than in t=1500. Thus, the price collaps is amplified in t=1500 because there is a longer period with a dominance of chartists (and an absense of fundamentalists).

Reply to issue 3:

There is a mistake in the representation of the results in figures 8 and 9. Instead of plotting the exchange rate and the random-walk-fundamental, I plotted the exchange rate and the zero line. This causes confusion, because one may interpret the zero line as the fundamental rate which is not the case. When looking at the time series for distortion in figures 8 and 9 (here is no mistake) one can see that distortions are decreasing when the tax is increased from 0% (figure 8) to 0.5% (figure 9). When you compare this to figure 10, you can see that distortion is not rising in the region from 0 to 0.005 (which means a 0.5% tax here). I think in order to avoid confusion I should scale tax rates with 100% in all figures.

Reply to issue 4:

I skipped to first 100 observations to avoid transitory effects. I will highlight this in the text.

Reply to issue 5:

The updated version (see link below) contains a much shorter introduction, with focus on agent-based models for the analysis of transaction taxes.

Reply to issue 6:

I will consider this.

Reply to issue 7:

I preserved the requirements in the new version. I find them also helpful.

Reply to issue 8:

I already adjusted them. Fundamental news are shocks to the fundamental rate, while non-fundamental news are shocks to the price-impact function.

Reply to issue 9:

I will consider this.

Reply to issue 10:

I will add this.

Reply to issue 11:

I will consider this.

Reply to issue 12:

I will consider this.

Below you can find an updated version of my paper.