A Paper On Housing Prices And Income

As I stated earlier in the week, it is imperative that you remember – income distribution is not a normal process.

By that, I mean it is not Gaussian; it does not take on the shape of a standard bell curve.

Like most samples when dealing with people, income distribution is wildly multimodal…that is to say, it takes on many localized humps, or peaks, each of which is the tallest point over some part of the domain when approaching from either direction. And, these distributions are erratic, changing frequently, so you can never put too much faith in them. They must be updated regularly, and only provide glimpses and snapshots at the state of affairs.

Now, I’ve taken the liberty of loading some information from the latest census. Unfortunately, and for obvious reasons, I do not have the Census Bureau’s data set, so anything I come up with here is an approximation of the real, continuous distribution I would have created had I had possession of said data – I have reverse engineered it from their conclusions as a close guess. It should, though, be accurate enough for the point I’m trying to make to you today.

(For reference, all data was taken off of page 33, Table A-1, titled Households by Total Money Income, Race, and Hispanic Origin of Householder. We are looking at the data of All Races).

Now, this provides a rough idea of the percentage of the population found in numerous layers of income level, where income is the domain. When observed without considering the density of each of the layers, attaching only a discrete value to each one, it looks something like this:

Notice that the data is not uniform (it appears so on the table the Census provides) because the domains attributed to each percentage are different sizes.

Now, when attempting to translate this information into a continuous probability density function, we can attain a rough estimate as follows:

As I stated before, we immediately see varying degrees of observations creates a sort of rough assemblage of peaks. Therefore, classical statistics and related approaches are not guaranteed to provide suitable results.

It is from this sort of data I can presume that a recovery in housing will not take on a gradually improving recovery.

It cannot be expected that housing prices will continue to pick up after that have first started.

But first we need to understand why this graph of income is relevant to the discussion of housing prices at all.

So remember, the housing crisis provides a very unique form of disruption in general market activity; one that is not regularly seen during the rest of your lifetime. It is so disruptive that I need to assume the resulting recession was ample enough to create a sort of start point.

Basically, I need to guess that for my following model, a majority of people, coming out of the recession, were like runners getting ready for a race. They all start at about the same point.

No one has massive savings reserves or other such wealth agglomerated, because if too many people weren’t affected by the recession, then they would be able to ignore it.

However, because the recession was so deep, and the apparent wealth of people, through equity prices, was impacted so greatly, I don’t think this assumption is to terrible.

The next story I’m going to have to sell you on is a growth of the first.

I generally think most people recognize the housing price sell off for what it is; a great opportunity.

Despite what financial journalists are spinning about, the housing price sell off is not occurring because people are afraid of further price collapse.

Honestly, even if they were, most people are sensible enough to understand that buying a home is a long term commitment that is to be nurtured through the bad times.

I get confirmation of this regularly, as random people I strike up conversations with on the street will even tell me of how now is the time to be buying a home.

If any of you have stories that strongly dismiss this observation of mine, please share them. I don’t envy being stricken with confirmation bias. However, for the meantime, I will march on, as I’m sure you understand.

So our remedial economics tells us that there are two conditions of declining prices; an overabundance of supply drowning demand, and a declining demand underwhelming existing supply.

However, there is of course a third and fourth relationship which affects housing prices; the medium of exchange and boundaries of contract.

Here, people just don’t have sufficient currency needed to enter into contracts for a house.

But as people accumulate the needed minimum savings to purchase homes, I believe that many if not most of them who can secure the financing will do so.

It is, after all, a great opportunity.

Which, as I said, makes this into something of a race; and the faster participants (those with larger incomes) can probably be expected to win.

Here is where income distribution comes into play. If I were to try and construct a time series that will appear in the future (as opposed to developing distributions from time series attained in the past), how would I go about that?

Why, I would need to construct a function, based on certain assumptions (here we have the income distribution, the correlation between incomes and savings, and of course the propensity to buy as quickly as possible) that would take random observations from our income distribution and map them across a time line.

Based on the distribution of income, the expected time series would therefore be a product of the density of incomes.

And, because income (and thereby savings) is what enables the purchase of homes, the relationship between income and time before purchase in inverse.

The wealthier a person, the closer to the time of the recession was that individual available to buy.

Now, to points should be addressed before moving on. And both stem from the fact that statistics are not concrete.

First, the wealthiest people will not always purchase when they can. Obviously, many of the super rich scorned homes as the prices were collapsing. They may also decide to spend their money on other things, leaving them with little savings to purchase a house. This means that our general inverse relationship is subject to error towards the beginning of the series.

Second, the poorest people will not always be relegated to last. Obviously, it is not outside the scope of possibility that someone of meager living had sufficient savings stashed away that they can jump towards the front of the pack. They may also sacrifice current expenditures, saving a disproportional amount of their incomes, to expedite the process beyond anything I would regularly hope for. This is an example of error towards the end of the series.

And both of those errors will redistribute themselves by either adding observations elsewhere in the series, or else creating pockets as the people-that-were refrain from buying at all.

Yet, outside of this white noise, I don’t believe anything I have said heretofore is so preposterous as to be admonished.

Now, let’s return to our 2009 income distribution and (without actually doing so) construct what any recovery in housing will probably look like:

Notice how at 2009, there was that sort of plateau of density in the upper layers? When comparing that region to the upper quartile (from the median of the data to the probable 75% of observations), also see that that plateau of incomes is well outside the inner quartile range, making it almost an outlier.

So we are seeing an uptick in housing sales. However, where in the distribution are those observations in the time series correlated most strongly to?

What if the uptick is still out here (uptick in green):

By that measure, housing sales may fail to improve from the latest “improving” sales numbers, for an extended period of time.

In order to really see a housing recovery, we need the majority of the population to get involved (or a serious contraction of housing supply). We need more than the outlying upper 25%; we need the American public, here:

And that’s what we need basing our discussion on data that is almost three years old. The present situation could actually be worse.

Because I don’t believe that income distribution in this country does look like what it did in 2009. The U.S. was hemorrhaging jobs all of that year, as I recall, and most of those jobs were the middle class.

Remember the income gap?

Income in this country could just as easily look something like this:

That would create a much greater spread of data, which in turn would create a much different time series.

Look at the quartile range on this example. After the wealthier participants, the density of the distribution could actually decrease! That would create another gap in sales on our time series.

If we are only just now here (again, uptick in green):

…then it is still quite possible to witness another drop off in housing sales before the actual recovery takes place.

In summary, I have great reservation about betting on a sustained housing recovery, at this time. This view also keeps well with my previous analysis in the space (on rentals), which is that home ownership levels, despite the turmoil in the market, are still elevated from historical perspective.

63-64% is far more standard than even the 66% we find ourselves at today. And its hard to envision a crisis that doesn’t take the home ownership level below historical levels. With the pent up mortgage foreclosure process, what happens if that rate drops below historical precedents?

In that last paper, I said I thought that stricter mortgage standards would exist for 2-3 years at minimum. If the uptick in housing contracts that’s occurring is based outside that upper quartile range I pointed out, then it has taken almost two years to get us there. How long will it take to make substantial inlays towards the inner quartile range?

Another 2 years? Longer, perhaps?

In general, I anticipate housing prices to stay depressed for another 2-4 years. However, when prices are getting ready to fully recover, there will be signs:

1. You’ll see citizen’s savings improve.
2. You may see mortgage down payment minimums lowered.
3. You will likely here of many younger individuals who have made the down payment (in my opinion, younger people are an excellent gauge of the housing market’s health; they will be needed to fill the lower end supply, as first time buyers).
4. The distressed homes and foreclosure rate will significantly decrease.
5. (This is an old secret passed down from my father) less homes will have un-mowed lawns.

In some combination, those things will accompany a recovery. A few of them alone may precede the turning point. All of them together will probably show it in hindsight.

If you enjoy the content at iBankCoin, please follow us on Twitter