crescet: waste and pine

"..man in short that man in brief in spite of the strides of alimentation and defecation is seen to waste and pine waste and pine.."  Lucky

The relationship between wealth and income is clearly strong.  There's an argument in economics that we do in fact consume based on our expectation on our lifetime income (under either a simplifying assumption of untrammelled friction-less borrowing from one time period to another or given a borrowing constraint as a function of wealth).  A (real) wealth process is in general replenished by the remnants of income minus consumption, per unit time.  It is also replenished by a rate of return on savings, and there's probably a jump process (in the sense quants use when modelling price action in derivatives pricing) on wealth - unexpected increases and decreases in wealth due to either an inheritance, an unexpected and large cost, etc.

In practice, the relative proportion of wealth over income (or expected income, or average income, smoothed over a lifetime) determines how much one can borrow, and one's consumption response function during times of economic hardship.  In other words, crescet drives your current (and expected future personal credit spread). If the amount you can borrow is always expressed to you as a percentage of your wealth,  then the associated borrowing cap and associated credit spread for loans are both functions of crescet.  Clearly it works well in a theorist's modelling of crescet if one can reasonably assume that there's a stable pattern of consumption based on a lifetime income  model.  It takes the variance out of the expected income process and allows for the possibility for doing a simpler lifetime crescet model.

The natural initial assumption, I think, is that consumption is based on a lifetime wealth process (which has embedded in it a lifetime income model).  It is also natural to assume that lending to consumers will always have a budget constraint based on some simple measurable proxy for the lifetime wealth process.  Current income appears to be the provable, easy to calculate proxy of choice, certainly in the western world.  

In the western world, it is a decent first approximation certainly for the last 70 years, to assume that the average person's wealth is held jointly in the property they live in, and in their pension.  However, when you look at this closely in the context of consumption smoothing and lifetime income, it becomes harder to make a distinction between wealth and sensible foregone consumption for future times.

Needless to say, the general flow of theory on consumption modelling goes like this: classical period economists model consumption largely as a function of interest rates.  Fisher introduces inter-temporal consumption and a budget constraint. Keynes in effect operates on the assumption that the average consumer is very much bound by the limit to borrow (i.e. he theoretically honours a real constraint on borrowing not present in theoretically pure models with frictionless borrowing).  He also, like lenders, approximates income as this year's income, and has no model for income to be shifted from one time to another (saving).  Modigliani added this element in the 1950s.  By far the biggest discontinuity in the lifetime income model is the fact of retirement, so in a sense, Modigliani introduces retirement to the model, and brings with that an ability to save and borrow.  I think this probably is a sign of the times.  In the early 20th century of Keynes, only about 10% of homes were privately owned.  By the 1950s of Modigliani's time, the US already had 50% home ownership.  So having a model which accounted for this significant fact of lumpy consumption in a person's life was an advance.

Friedman further made a sub-distinction between that fraction of 'reliable' and 'windfall' income, and considered the former more determinant in the consumer's life.  Windfall income adjustments (a legacy from a rich relative, a lottery win, a sudden hospital bill, a windfall tax) ought to have a net effect on one's wealth, depending on how that is consumed or saved.

One final chronological piece of background - the 1930s of course foregrounded the problem of persistent unemployment - a phenomenon not 'solved' by adjusting the real interest rate.  This leads Keynes to pursue aggregate consumption, including the less controversial personal consumption function (my current focus) and the much more variable investment function.

Lastly the rational expectations mob arrive on the scene to point out that if the consumer is doing all this good modelling and smoothing of lifetime consumption, then any actual changes to consumption would therefore have to be random (meaning unpredictable).  There's something quite beautiful about that step, even though the assumption made in it is initially hard to believe.