Change in Tax Rate over Time

Terra Taxes are a percentage fee (between 0.1% and 1%) charged on transactions on the network. These fees act as a stability mechanism by keeping block validators (miners) incentivised to maintain participating in the protocol. The tax rate changes each epoch to provide the right incentives for miners. An epoch on terra is 100,800 blocks - around 1 week at the target block time of 6 seconds. The graph below shows the Terra Tax Rate % over the last 10 epochs:

What Drives Changes in Tax Rate?

Tax rate makes a bit more sense when we understand the reasons for it changing. Miners are exposed to market price risk and to fluctuations in network demand. This makes their income uncertain, whereas their costs (primarily node hosting costs) are relatively fixed. In a competitive node environment, with over 100 validators competing for rewards, margins can get squeezed. Terra relies on miners to play an important role in the network so there are stability mechanisms to ensure that miner rewards are long-term stable and contribute to the growth of the system.

The tax rate mechanism is based on a couple of simple principles:

• When mining rewards are decreasing, the tax rate increases (and vice-versa) to ensure reward stability when there are short-term variations in rewards
• Mining rewards grow steadily over the long term to encourage long-term investment

The implementation detail is a bit more complex, so we will drill down into the math:

Tax Rate Calculations

As mentioned above, the tax rate is recalculated and published to the chain at the end of each epoch. The tax rate in the new epoch is a function of the old tax rate, and is as follows:

New Tax Rate = (Old Tax Rate) * (Mining Increment factor) * (LT Tax Reward Rate / ST Tax Reward Rate)

Here we see the simple principles mentioned above:

• LT Tax Reward Rate / ST Tax Reward Rate makes the tax rate go up if ST rewards are lower than LT rewards (and vice-versa). This boost miner income when rewards decrease, and pares it back when rewards go higher due to network activity.
• Mining Increment is greater than 1 which steadily increases the tax rate over time, and hence mining rewards.

Extra nerdy implemetation details

In the above tax rate calculation, the parameters are calculated by:

• Tax Reward Rates - total tax rewards over the epoch divided by the quantity of staked LUNA at the end of the epoch. Rewards are denominated in SDR (Special Drawing Rights, an international reserve currency)
• LT Reward Rate - the yearly rolling arithmetic average of the reward rates (52 epochs)
• ST Reward Rate - the monthly rolling arithmetic average of the reward rates (4 epocs)
• Mining Increment Factor - this is set to 1.07 in the protocol

A note on Seigniorage

Mining rewards include both tax rewards (from transactions) and seigniorage rewards (from voting on oracle prices). The amount of seigniorage assigned to miners is governed by the reward weight parameter which is also set at the end of each epoch. The reward weight has been set to zero since March 2021 - this indicates that the miners get zero seigniorage. For the purposes of this analysis we will ignore it.

Revisiting Tax Rate

Now we know how the tax rate changes work, let's look at the data. First up is the tax rate graph shown above, repeated for comparison with the graph below it. The graph below the tax rate chart shows the LT unit mining rewards (pale blue) and the ST unit mining rewards (dark blue). You'll notice that early in the this 10 epoch timespan the short term rewards were well above the long term rewards. The protocol responded to this and pushed down the tax rate to compensate, as is seen through to the 6th epoch in the tax rate chart. At this point, there was a flippening of the ST and LT tax rewards - the ST rewards fell below the long term average, dropping miner revenue. The protocol again responded, pushing the tax rate steadily up to around 0.45%.

A quick look at staked LUNA

You'll remember from above that our rewards calculations are unit rates - rewards divided by the total staked LUNA in the epoch. The graph below shows the total staked LUNA over the last 10 epochs. This has been steadily increasing, apart from a big dip in epoch 7. Looking at the unit rewards and tax rate graphs, there doesn't appear to be any discernible impact on things from this change in staked LUNA. The assumption is that rewards also decreased during this time and the unit rate didn't change much. Another factor will be the averaging - the tax rate changes based on the 4 week and 52 week reward rates, so changes in 1 week will have limited impact.

Conclusions

Terra has been carefully designed to provide the right incentives for participants so that there is long term health and growth in the system. In particular, the tax rate is a protocol mechanism to ensure stable rewards for miners, which should incentivise long term participation in network consensus. We have dived into the details of how this mechanism works, and seen how macro factors influence the tax rate in support of the design principles.