Solving one problem with Progressive Taxation: adding memory effects

2011 October 13
by Daniel Lakeland

In my post from yesterday I talked about how progressive taxation hurts people we probably don’t want to hurt, people who are entrepreneurial or who delay their income by increasing their education and similar situations. One of the reasons the progressive tax codes are so bad for these groups is that they are memory free, they treat two people with high incomes this year the same regardless of what their historical situation was. For example a person who spent many years in graduate school to become an expert at something that pays very well and is in their first year of reaping the rewards is taxed the same as someone who had both an enormous trust fund income for many years as well as a high paying job,  and recently lost their job so their income is down to the level that the grad school graduate is so happy to be at.

One way to deal with this issue is to tax wealth rather than income. This is in general a more reasonable way to tax people as wealth is associated with ability to consume and with political power, whereas income is more associated with how your wealth and consumption are changing this year. But there are practical difficulties in taxing wealth, it’s easier to hide wealth than income, and its harder to measure wealth when that wealth includes things which are illiquid (such as real estate, art collections, non-publicly-traded stock or whatever).

One way to deal with this problem is to make some kind of approximation to taxation of wealth. For example we could tax the integral of income minus some “minimal consumption” which represents what we think people need to consume to live without serious hardship. For example $$W_{tax} = \int_{0}^T Inc(t) – C_{min}(t) dt$$ where $$W_{tax}$$ is taxable wealth, $$Inc(t)$$ is income, and $$C_{min} = F + H + Hc + E$$ where F is food, H is housing and utilities, Hc is health care, and E is education. In this scenario we could all argue about what goes into $$C_{min}$$ and to a great degree we could also argue about $$Inc(t)$$.

For example, currently we have capital gains income which is taxed at a lower rate, and is only taxed upon the sale and “realization” of the capital gain. This is a pretty stupid way to tax capital gains in my opinion. First it discourages people from allocating their wealth in a more optimal way, since each transaction that might improve the allocation is taxed, and second although the goal of taxing capital gains at a lower rate is to encourage savings, in fact it is a highly regressive (as opposed to progressive) tax since people who are quite rich get most of their income from some form of capital gains, since more of the tax burden is then shifted to “earned” income, there is less money available for the less wealthy people to save.

My initial guess is that we would do quite well to organize taxation as follows:

  1. Mark-to-market all major liquid capital assets annually. This means stocks, bonds, derivatives, and the book value of non-publicly traded stocks, as well as some standard measure of the equity change for real estate (perhaps treat a primary residence somewhat specially). For the uber-wealthy with big art collections and unique homes whose value is hard to determine perhaps there could be a separate law dealing with these kinds of capital assets.
  2. Annual earned income would be calculated at the end of the year as it currently is from W2 etc.
  3. Calculate the current year’s (year n) taxable income as $$I_{t_n} = I_{t_{n-1}} (s) + I_n (1-s)$$ where $$s = e^{-1/T}$$ where T is a characteristic time. A good choice of characteristic time might be around 1/10 of a typical lifetime earnings duration (say age 65 you retire, and age 20 you typically start earning, so 45/10 = 4.5 years and $$s = e^{-1/4.5} \approx 0.8$$).

The above method is what’s called an exponential weighted moving average. You take the moving average from the last period, weight it by some amount s, and then add the new increment weighted by (1-s). It averages your income over all of your income history, and its effect can be seen by using exponential weighted smoothing on a stock price, it’s a very common technique and you can see an example for the exchange traded fund “SPY” with 100, 300, and 450 day exponential weighted moving averages over a 5 year period. The longer the period, the smoother the curve. This is an exponentially weighted moving average of the total value (think wealth) so something like its derivative would be something like exponentially weighted moving average of income.

This method has several advantages:

  1. It is history dependent, so it taxes people based on not their current income, but a measure similar to the integral of income I mentioned before.
  2. It is very easy to calculate, and easy to explain on a tax form.
  3. It allows us to tax people who have significant capital gains based on their trend in capital accumulation, and eliminates much of the noise caused by year to year fluctuations. (at the same time, if you lose a lot in the market it will take time before you stop being taxed on your previous earnings, so there is some need to deal with severe market downturns, where people may not have the ability to pay. That’s nothing new though, there have always been people who get rich, owe a lot of taxes, and then go bankrupt.).
  4. It eliminates barriers to capital reallocation. People can simply buy and sell their assets as they like, the tax is not associated with transactions.
  5. The time scale for exponential weighting is matched to the time scale of our lives, and the time delay for growing income to be seen in the tax burden gives an incentive to improve ones income.
  6. By including capital gains in income it taxes people in a similar manner regardless of the source of their wealth accumulation, but by averaging over history it also offers an incentive to save and optimize allocation since growth is not taxed immediately but rather over time.

It’s not perfect I’m sure, but it is a realistic and simple way to modify the basic structure of income tax to distribute the tax in a standard way over all people regardless of how they earn their wealth, which also improves the incentive to invest in the future and reap the rewards of education and entrepreneurship.


2 Responses
  1. Daniel Lakeland
    October 13, 2011

    Note also that marking assets to market annually doesn’t have to mean taking the price on the last trading day in the year, it could for example take the average of the prices on the last trading day of each month during the year or something like that. We want a measure which doesn’t have a lot of noise in it and a single day’s price is not a good measure.

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