# Chris Natoli

## Do higher Bitcoin transaction fees lead to higher volatility?

published 26 January 2018

Abstract: Yeah, seems like it. A basic regression analysis demonstrates positive, statistically significant correlation between Bitcoin transaction fees and volatility with non-negligible effect sizes. This suggests that adoption of SegWit and the Lightning Network should decrease volatility in BTC/USD price.

During the 2016 Democratic primary, many neoliberals criticized Bernie Sanders’s plan to fund free public higher education with a financial transaction tax, arguing that it would increase volatility in financial markets. The narrative behind their criticism is that such a tax would discourage informed investors – who usually bring stability to financial markets – from trading. However, many economists from Keynes to Joseph Stiglitz believe the opposite narrative: a financial transaction tax would discourage speculators, who add noise to the usual fluctuations in an asset’s value, and would thus decrease volatility. Different empirical studies and theoretical models yield both positive and negative correlations.1

Judging by a quick scroll through Google Scholar, most empirical studies contrast the affected financial markets before and after the imposition (or elimination) of a financial transaction tax. This inevitably divides time into two discrete segments and represents the tax as a binary variable (on/off) rather than a continuous one, thus limiting the power of the study. But since Bitcoin transaction fees fluctuate constantly, they can serve as a proxy for financial transaction taxes while remaining a continuous variable. Moreover, they provide a new data source for studying the question of financial transaction taxes.

Of course, the relationship between the volatility of BTC/USD and Bitcoin transaction fees is worth studying in its own right, especially given the (perhaps stubbornly) slow adoption of SegWit and the Lightning Network, which would help reduce transaction fees.

### Regression

To test the relationship between volatility and Bitcoin transaction fees, I regress a given day’s volatility on the average transaction fee that day and the previous day’s volatility, as a control variable.2 To be precise, let $V_t$ be the volatility (i.e., variance) of log-returns of BTC/USD over a given day $t$. Since transaction fees can be expressed in terms of BTC or USD, and since the proportion BTC/USD obviously varies, we need to treat them separately. Let $F_t^{\mathrm{BTC}}$ be the average transaction fee on day $t$ in terms of USD, and let $F_t^{\mathrm{USD}}$ be in terms of BTC. I estimate one model where transaction fees are in terms of BTC: $$V_t=\beta_0+\beta_1F_t^{\mathrm{BTC}}+\beta_2V_{t-1}.$$

Coefficient $p$-value 95% confidence interval
Intercept −2.107·10−6 0.350 [−6.53·10−6, 2.31·10−6]
Transaction fee $F_t^{\mathrm{BTC}}$
in BTC
0.0235 <10−15 [0.018, 0.029]
Lag of volatility $V_{t-1}$ 0.3830 <10−15 [0.319, 0.447]

I also estimate a model where transaction fees are in terms of USD: $$V_t=\gamma_0+\gamma_1F_t^{\mathrm{USD}}+\gamma_2V_{t-1}.$$

Coefficient $p$-value 95% confidence interval
Intercept 7.542·10−6 <10−5 [4.29·10−6, 1.08·10−6]
Transaction fee $F_t^{\mathrm{USD}}$
in USD
1.791·10−6 <10−15 [1.38·10−6, 2.20·10−6]
Lag of volatility $V_{t-1}$ 0.3726 <10−15 [0.308, 0.438]

Note that both regressions use data from GDAX and Quandl, spanning from 31 December 2016 to 21 January 2018, i.e., 753 datapoints. The volatility was computed from 15-minute returns during the same period of time. All the code and data, as well as diagnostic plots to check for collinearity, are available on my GitHub.

### Results

The first model, in which transaction fees are in terms of BTC, shows positive, statistically significant effects on volatility from both transaction fees and the previous day’s volatility. In fact, the effects were so statistically significant (i.e., the $p$-values were so low) that I was initially suspicious. In such situations, everyone’s favorite academic statistician, Andrew Gelman, argues to focus on effect sizes, i.e., the coefficients. Here, a 0.001 BTC increase in the transaction fee (which has ranged between 0 and 0.004 BTC in the last couple years) is associated with an increase in volatility by 2.35·10−5, which is sizeable since the mean volatility in the past couple years is 2.12·10−5. Even at the lower bound of the 95% confidence interval, a 0.001 BTC increase almost doubles the average volatility. So the correlation between volatility and transaction fees is both significant in effect size and statistically signicant.

The second model, in which transaction fees are in terms of USD, shows similar results: the $p$-values are again very low, but the effect size is still non-negligible. A 10 USD increase in the transaction fee (which has historically been as high as 60 USD and, in late December 2017, had fluctuated by over 10 USD from one day to the next) is associated with a 1.791·10−5 increase in volatility. The effect remains non-negligible at the lower bound for the 95% confidence interval.

Of course, further study of how well Bitcoin transaction fees serve as a proxy for financial transaction taxes is a worthwhile extension of this preliminary research. Regardless, these results suggest that the increasing adoption of SegWit and the Lightning Network should help stabilize the BTC/USD market.

### Footnotes

1. As usual with the dismal science, determining which economists to trust is as much a question of evaluating their competence as a scientist and a statistician as it is a question of their politics.^

2. I also tried BTC/USD price, the second lag $V_{t-2}$ of volatility, and the number of transactions that day as regressors. The first two were not statistically significant, while the number of transactions was significant ($p=0.022$ and $p=0.009$, respectively) but had negligible effect sizes (coefficients were on the order of 10−11).^