Personal savings rate

[David]

Do you guys have any suggestions about how the personal savings rate should be simulated in the game?

Personal savings rate will determine how much of a person's salary will go to bank deposits.

Note: the following are other posts on this forum related to this topic:
http://www.capitalismlab.com/forum/view ... 497#p11650

http://www.capitalismlab.com/forum/view ... 9121#p8872

[counting]

I've planned to write something about that when I start the thread of "Capitalism and its foundation in monetary economics". But it's not a short one. And honestly a very complex issue.

The simplest answer is that the trend has correlation with many macroeconomic variables, like unemployment rate, income brackets, inflation, even consumer sentiments, but also sociology factors like consumption structure, even culture elements like the difference by regions due to customs. And from micro behavior perspective it has deep root with many motives behind psychology. But current general consensus is that its not an external variable, and factors effecting personal savings rate has long-term and lasting effect to it.

And in a broad sense, its just an expression of delay consumptions, where the boundary may not be easily identify (like how long does a deposit need to stay to be considered "savings"). Modern electronic transaction also make "savings" have different meanings in lots of ways. There have been studies about the wide use of ATM, has negative correlation with of savings rate paradoxically, since people carries less real notes physically, and treated ATM as the extension of pockets, thus harder to control the impose of purchasing, and with wide variates of financial tools, people don't tend to hold cash and cash equivalent assets as pure savings due to convenient e-commerce options and innovative financial instruments available (the shadow banking system).

In general, most modern theory about savings rate derived from a very simple formula C = Y - S. Consumptions is the difference between income and savings, and an iteration model of savings rate s(t) = S(t)/Y(t). (Defined by Milton Friedman). From here, many variations can be formulated and Friedman himself pose an assumption that s(t) will reach a stable equilibrium 1-k, where k is a constant, the life time propensity to consume out of permanent income. And a dynamic adaptive model of C' = r * (kY - C). C' is the next iteration Consumption, based on an adaption rate of r. Thus S' = Y' + r * ( (1-k)Y - S). where s' = r(1-k) - rs + (1-s)Y'/Y. And this means savings rate has an inherent equilibrium value s, but is subjected to permanent changes and differences by regions/cultures/technologies/etc in the long run, with lifetime consume tendency k as the primary factor, and a short-term adaptive rate of r, based on the fluctuation of real income (Y'/Y). There is no need to model the behavior exactly like this, but it could be a start, where it's easy to expand and add different factors into an adaptive model.

[counting]

What makes this issue complex and some what controversial is not because of the complex physiological reasons behind "savings", but the mirror side of the savings - consumption. Since savings is traditionally treated as the "residual" of consumption. And since consumption is the base of demand, hence it's obviously a very fundamental issue need to be addressed. However, economists always know the importance of accumulation, hence there are some hypothesis focused more on the wealth side than the demand side.

Two of the famous hypothesis are PIH (Permanent Income Hypothesis developed by Milton Friedman as the extension of the formula I mentioned above), and LCH (Life-Cycle Hypothesis). There are many other consumption and savings related hypothesis but these 2 are probably the easiest to implement in simulation but with enough complexity to generate non-linear complex macro-behaviors. There are variations within these hypothesis to modify them, and experiments trying to determine which fit the real world economic behaviors. But as I mentioned before, decades of researches only tell us they are inherent complex and people tend to base their decision with many different motives, and even macro-behaviors could be a combination of multiple underlining mechanics. There are computational economics experiences trying to model agents based on different hypothesis, even combination of many, but their results are usually not conclusive, and even conflicting in different studies. IMO, if someone trying to mimic the complexity of consumption behavior (and in the process savings), probably a weighted ratio combination is probably the easiest. Try to model several different hypothesis (even the most basic one), and assign different bracket of population belong to them, and get an aggregated result. One can easily image with a lower education or living standard city, more people would belong to simpler model bracket (like the simplest, a fixed forced saving ratio), than complex model.

BTW, it would be a little difficult to transit LCH into mathematical model than PIH. LCH depends a lot on profiles of the agents and their history, hence a statistical background of wealth and age of the demographic is required to build a model using LCH, otherwise it would required many agents to simulate each individual (or representative agents).