association-list

I was bored tonight and pro­cras­ti­nat­ing, as per usual, so I decided to toy around with some simple sim­u­la­tions. The sub­ject for these exper­i­ments was tax­a­tion, which I’m sure every­one and their dog finds wildly excit­ing, but these kinds of things are impor­tant, and if my life was excit­ing I wouldn’t be writ­ing simulations.

The setup is this; take some fixed number of indi­vid­u­als, toss them into bins accord­ing to a normal dis­tri­b­u­tion (Likely too narrow, really, as a lot of them end up empty. Might need to raise my sigma?), then crudely apply the effects of income, infla­tion, tax­a­tion, random chance, etc. The tax­a­tion comes in two modes. Pro­gres­sive, rising steeply towards the top, and flat for income and cap­i­tal gains. I eye­balled the curve for pro­gres­sive, since I didn’t want to cal­cu­lat­ing each time, and I was too lazy to cal­cu­late it in the first place. Rates are 95% for the top bracket.

Some stats:

• Twenty bins in 5000 unit incre­ments, start­ing at 20000.
• 10000 + 0 – 10000 start­ing invest­ment capital.
• 10000 unit tax brack­ets (at the start).
• Infla­tion fixed at 4% per year, and brack­ets scale with it.
• Yearly wage increase is infla­tion +- 2%, with a 5% chance of losing or gain­ing 0 – 10% to sim­u­late job changes.
• Cap­i­tal gain is 5% if your cap­i­tal is below a cer­tain point, 8% above that, to sim­u­late incred­i­bly crudely that if you have more money, you have access to a better class of invest­ments. Also there is a 10% chance of losing or gain­ing 0 – 20% to sim­u­late above or below aver­age years.
• No one ever dies or has major life changes.
• Income is the sum of your post-​​tax wages and post tax invest­ment cap­i­tal for bracket cal­cu­la­tion purposes.

Ini­tial results are what you would expect, if you’re rea­son­ably famil­iar with the theory. Flat taxes tend to spread people out over time, even­tu­ally pop­ping people off the top of the sim­u­la­tion and drop­ping them off the bottom.

Pro­gres­sive taxes tend to squeeze people towards a stable middle, with out­liers being fairly quickly cor­rected. It’s crit­i­cal to lock the brack­ets to infla­tion or every­one falls off of the bottom in short order.

Obser­va­tions:

• Cap­i­tal tends to vanish if you have very little of it to start. At first, I started each person with 0 – 20000 unit of invest­ment capi­tol. After a few thou­sand iter­a­tions, the vast major­ity of people had noth­ing. I’m fairly sure that this is a mod­el­ing issue.
• Pro­gram­ming to learn some­thing new is a great way to remem­ber why you started doing it in the first place.
• This is likely the least inter­est­ing post I’ve ever done. I haven’t defamed a single person!

If anyone is inter­ested in look­ing at the code, or has a sug­ges­tion for refin­ing the model, drop me a note. I’d have to clean the code up a little, but it’s not shame­fully messy.