The essential idea is to find a measure similar to power and strength (the statistical terminology used here). So essentially what I am doing is figuring out a way to find out what is happening in an economy and how do we manage to figure out whether or not there was indeed a bubble. I have posted several things about this in the past and am still working on better ways to finger this little issue out. That is when the idea of measuring the power and strength of the economy.
It is an interesting question on how to measure this within an economy itself. What you are looking for is future potential versus current conditions. Most people might say lets use regression and predict off of the model that we have created but is that the correct way to measure the economy...I might say no.
The issue with regression is until you mix in negatively effecting terms, you are missing a lot of the model and simply shrinking epsilon is not describing what is going on in the economy. Considering this is very interesting because we have missed so many, in fact every major economic event trying to use complex regressions to predict the future value of something and I contend that this is more adequate on a microeconomic level and not adequate enough to measure on a macroeconomic level. So let us simplify things and look at simpler mathematics for a minute.
Let us begin to descibe the model...
The idea is to take the real economic data and simply put it over the nominal economic data. What this will give you is the potential of the actual economy. That is it! Nice little theory isn't it...it is just simple division but let us consider exactly how this all works out and I will try to debunk some of the negatives of this little model.
The idea is so simple but very powerful. What it essentially measures is the consumers ability to buy by the real over the nominal effects. This model adequately can show hyper-inflation, normal inflation, deflation and what it really shows is the consumers ability for future purchases and can show if understood correctly, the future impact of economic decisions and economic indicators.
In an inflationary period, nominal is growing faster than real and thus the potential of the economy is losing strength. If nominal is growing faster than real then the economy is not growing at all but is actually shrinking in its ability to grow. In the case of hyperinflation, you can readily understand, even a 10th grader would understand that the asymptotic lower bound of this is zero. This means that the economy will not grown until the nominal is gained control of over the real. This is a perfect scenario towards finding out the future potential of an economy.
Why this is good and not perfect is that as the economy reaches the asyptotic lower bound, the future potentcy of the economy is being lost and this describes perfectly what happens in a economy as it grows towards the future. This formulai never reaches zero because there is always a chance of future economic growth. Even countries such as Bolivia with its 1000% daily inflation during the bad days still has future economic potential it is just that things are out of whack and need to be corrected before the economy can grow again.
Consider the housing market for a minute...in the case of this, nominal growth was far out-pacing realistic grownt potential. The price was out-pacing the actual growth by a large margin and the way this can be measured specifically is raising your function to the growth rate of the populous, or market populous. In this case the market populous, those adequately able to afford a house was not growing at all but sales were increasing incrementally. The growth rate in some areas per annum was above 10%. This does not show a strengthening of the economic condition but instead a weakening of the condition.
Some of this is being written "on the fly"...the n idea is a little iffy as I think about it more but the rest is strong.
Actually, as I think about it more, if you raise each term in the denominator to the inverse power of the growth rate of the population, this should work itself out. As the population is growing it is strengthening the future potential of the economy itself. If the growth rate of the population is out pacing the growth rate of nominal gdp, then the economy is strengthening. Further, if the population is declining then the economy is weakening.
Let me stress here as I think about this, this model is showing the future potential of the economy not the current condition of economic affairs.
Essentially this should be viewed as future consumer sentiment. This model works because it is describing what consumer sentiment is going to be not what it actaully is. This model is not going to give you real values as to what is going to happen in the economy but what it is going to give you is what is likely going to happen over the next non-specific period in the economy.
This simple model can be used in any scenario to find out what is going on in an economy. In particular, in the housing market if you look at the data, I am sure what you will find, as I do not have ready access to the data I need to prove this, is that as the data tends towards the asymptotic lower bound then the future potential of the market is decreasing. In the housing market, the populous adequately able to buy a house was not growing as income was not growing by significant measure but the nominal price of a house was growing.
I am bored right now and will revisit this thought experiment later. I am leaving out one economic argument from explation for a specific reason...and belive me there is a very good reason for it. I will kill you with the explanation of why!