saving vs. consumption as default actions

admin — Tue, 17 Mar 2009 20:23:08 +0000

Lately, for good reason, there has been many advice columns telling people how to plan for personal financial goals. It always used to boggle my mind when I heard exhortations to save, where “save” is used in the sense of an action among which to choose, parallel to things like “invest” or “work”. Until I realized, some years back, that to save is a parallel action of choice to some.

I guess I’ve never had that notion. To me, saving isn’t something to do, it’s what happens by itself, by default, if you do nothing. How can you “invest” or do anything else without already having saved? It’s more like the base case underlying most other actions that occur at a hierarchically higher level. This notion is tightly coupled with the other notion that to borrow is only a time shift where you temporarily go into negative territory for a short time out of necessity (like in an emergency). This is typically risk averse behavior.

Now let’s turn to the other model of behavior, where things are swapped around. Here, consumption is the default. To consume is what happens if you do nothing; that is the raison d’etre. All other actions service that need. In other words, why bother to “save” or “invest” or “work” if you do not consume? See how this is inverted? Again, this is tightly coupled with the notion that borrowing is a tool of persistent leverage for greater return. This is typically risk taking behavior, in technical parlance of course.

To make the cases even more distinct, here are two graphs of model behaviors:

“savers”
save save->invest->save save->consume }" src="wp-content/cache/3bfd3f59a8d6581378e6899fa2bc7124.png" />

“consumers”
consume save->consume work->consume }" src="wp-content/cache/2bd2034da4ff178e165fd22421c3ec9e.png" />

So people try to analyze why East Asia saves so much and why China especially cannot get internal demand going due to excess savings, whether it’s because of the lack of a social safety net, or because of an inequitable distribution of wealth. Yes, these have some effects, but no. I don’t think those are why. It has to do with how personal financial behavior is internalized from the past, as much as influenced by conditions in the present. I think risk averse behavior is ingrained into people in times of scarcity (credit scarcity or capital scarcity) and how long this behavior lasts depends on the severity of a downturn and the subsequent period of prosperity. (As an aside, it can be argued that risk taking behavior isn’t entirely risk taking behavior but partly a bad estimation of the actual risk.)

A little Markovian problem

admin — Sun, 29 Oct 2006 20:18:39 +0000

Here it is:

A has a fair coin and B has a fair coin. They flip coins together, but only keep track of their own sequences of heads and tails. A stops if the sequence “HHT” appears. B stops if the sequence “HTH” appears. Which player is more likely to stop first?

While it would first appear that any 3-flip sequence is equally likely and so neither A nor B is more likely to stop before the other, this is wrong. The eight 3-flip sequences are only equally likely when taken independently of the remaining sequence context. By context, I mean there is a time origin in this problem and there is memory from the stopping 3-flip sequence that leads all the way back to it.

The answer is found if we draw the state diagram of the game for each player.

Player A
H [label=H] 0 -> 0 [label=T] H -> HH [label=H] H -> 0 [label=T] HH -> HH [label=H] HH -> HHT [label=T] }" src="wp-content/cache/f151847dd4f5adb6d5a138ee4e318e12.png" />

Player B
H [label=H] 0 -> 0 [label=T] H -> H [label=H] H -> HT [label=T] HT -> HTH [label=H] HT -> 0 [label=T] }" src="wp-content/cache/df43149372f6033610ee6b9ee0c87df5.png" />

They are pretty much the same, except A’s diagram has a transition that backtracks by one state where the analogous transition on B’s diagram backtracks by two. So indeed, A is more likely to stop first.

An interesting thing happens if we let A and B continue flipping even after they are supposed to stop. This changes the destination of one transition in each state diagram. Now the two diagrams look more similar.

Player A
H [label=H] 0 -> 0 [label=T] H -> HH [label=H] H -> 0 [label=T] HH -> HH [label=H] HH -> 0 [label=T color=blue] }" src="wp-content/cache/1f05e52fe69f93b1f3ca986f4916b9b8.png" />

Player B
H [label=H] 0 -> 0 [label=T] H -> H [label=H] H -> HT [label=T] HT -> H [label=H color=blue] HT -> 0 [label=T] }" src="wp-content/cache/2485278455bd040486cf9dd6cb8c2592.png" />

In fact, they are equivalent (after a rotational shift of the states). So asymptotically, the sequence “HTH” occurs just as frequently as “HHT”.

If we look at this a little more carefully, we find that it takes on average 8 flips to see the first “HHT” while it takes an average of 10 flips to see the first “HTH”. After that, however, both subsequences occur at a rate of every 8 flips (overlapping frames allowed), which of course makes perfect sense, since there are 8 such 3-flip sequences.

Some stuff » digraph

saving vs. consumption as default actions

A little Markovian problem