how to buy a house

with all the turmoil, it is good to think about how houses are bought in the US
Now

We'll do a first order estimate, it scales linearly with changes in income and is an adequate approximation to understand how things work. Now.

Unless you have a lot of cash, you need to get a loan to buy a house.
This is typically a fixed rate loan, secured by the house as collateral, and we'll estimate an 8% interest. Simple interest will do as first order estimate. Doing the full compound estimate is trivial and an exercise for the reader. The loan term will be 15 or 30 years typically. Long enough that the initial payment is dominated by the interest, although the full amount will be paid off over that period.

We will assume the approximate median household income in the US at $48,000 per year.
You will need documentation for that income, a year or three of paystubs or tax returns.
You will need to bring 20% cash down to get the loan. At least. This must not be an informal loan or a short term "gift", it must be your own money as documented by bank statement from a saving account or similar, over a period of say six months.

As a rule, you can borrow no more than about three times your income, so your loan can be for $144,000.
With a minumum 20% downpayment, that means you can buy a $180,000 dollar house.

The loan payments will be a little over $12,000 per year, or a little over $1000 per month. This is 25% of your gross income, or roughly 1/3 of after tax income for typical situations in this income bracket. There will also be local taxes and insurance, the mortgage company will require you to carry insurance.

To get a downpayment of $36,000 from earnings, starting from nothing, you need to find a living situation where rent is much less than the mortgage - it should be possible to find lower grade housing at half the mortgage you will be paying, and with no incremental effort you can save $600 per month, or $7,200 per year.
It will then take you 5 years to save the downpayment. Less if you have long term savings or unearned income, or if you really scrimp. I'm ignoring interest on savings as they tend to track mean housing appreciation. This is not the sort of money that can be safely invested in investments with higher rate of returns and higher risk.

That is what you can afford.

Fixed rate loans typically do not have prepayment penalties on principal, so as your income increases, you may accelerate the payment, and expect to maybe pay off the house in 10-20 years for a 15-30 year loan.
With modest appreciation of 3% per year, after ten years your house would be worth $240,000 and you would own it outright, if you acted conservatively.

If your situation has changed at this point, you can now sell the house and have about $200,000 in downpayment, after transaction costs. If your income has also increased at 3% per year, you can now afford a $240,000 mortgage and have 40% downpayment - so you can move up to a house worth about $400,000, but not much more, and own it holding substantial equity from the start. It will take another decade or three to payoff the new bigger house fully.
This is a typical pattern, modulo to forced moves due to job or family changes.

The US is extremely unlikely to see the sort of housing market there has been for the last decade (two decades in CA and NYC). For at least a generation.
Median housing prices will be at about $200,000 for smaller homes, and only a few percent of homes will be at much over $500,000.

The only way around this arithmetic is to either bring a larger downpayment, through equity, inheritance or serendiptity; or to have significant unearned income.
The whole thing scales with inflation - if wages and prices track each other through inflation cycle.

Note, this also informs you how to behave for different housing price gradients:

- if housing prices are stable or rising slowly, then you should buy when you have the downpayment and build equity. If you think you are likely to have to move in less than three years, then don't buy, moving too soon leads to a loss due to transaction costs.

- if housing prices are rising rapidly, then buy as soon as you can, using any gimmick you can, because otherwise entry into the market gets increasingly hard with time. The prices rise faster than you can build rational downpayment, and price rises build free equity if you get in before or during the upswing. The bubble behaviour is rational, short term.
Unless you think prices are going to come down before you can pay off some of the principal, or sell and cash in the equity.

- if prices are declining, do not buy, rent. Unless you are willing to access the short term paper loss and inability to sell in case of emergency. This is rational if you are looking for a long term abode where you have the control that comes with ownership and a strong rational expectation for not having to move until some time after prices stabilise or rise again, or after you have paid most of the principal. Note that this lowers demand for housing purchases in the aggregate, suppressing prices further. This generally continues until the cost to rent equivalent housing becomes as expensive as buying. With some lag due to market overshoot, lenders overanticipating trends, and the need for renters to (re)build savings for downpayment.

From which we also conclude that there is a positive feedback instabilities in housing markets, both those which are declining and rising, provided the change is significantly different from the long term median.

Hoocouldanode.

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When I was first thinking about buying a house, I bought a Home Buying for Dummies book. Despite the ever annoyingly insulting title, but book was filled with very good information...and frightening...enough so that I put the book on the shelf and postponed the house search.

Four months later (after yet another remarkable conflict with our landlord), I dusted the book off, read it thoroughly, and proceeded in the house purchasing process.

This simple educational process was unbelievably valuable. In contrast, talking to other people who had bought houses really wasn't - people who have gone through the process tended to be very biased and defended the worst of decisions as if they didn't want to look stupid for having made them.

While our current dilemma has been caused by greed of many different parties, I think basic education could have averted many of these problems.

Self initiative is important and I'm glad I frightened myself into learning as much as I could before diving into the purchasing process. But as I grow older, I can't help but think one basic "life skills" class in high school that covered items like major purchases, loans, dangers of credit card debt, etc. would at least have sparked a light bulb in the heads of folks who ultimately didn't know better in making bad decisions.

Steinn --

Some of these numbers seem a bit suspect. How exactly can you save $7200/year out of $12k/yr in mortgage costs by renting instead? And is it really reasonable to expect to spend only spend 25% of your salary on mortgage in the first year of a thirty-year fixed mortgage? Especially if you are in a market with inflexible supply and plenty of people willing to tighten the belt harder in order to compete against you?

You've also left out the huge factor of intergenerational wealth transfer. Since inheritance taxes were essentially eliminated in this country (except for a tiny fraction of the wealthiest), much of the accumulated housing wealth is recycled into the next generation.

And keep in mind that the median household income of home buyers is substantially higher than $48k/yr, since the poor typically rent, and the median incomes in the most talked-about "bubble" markets are well above national averages. Buying a house in Aspen or a mile or two from the Pacific is not something a "typical" household can probably ever expect to be able to do. And it doesn't seem irrational for a highly skilled worker to "invest" heavily in moving to Silicon Valley or some similar area where his or her talents will be compensated better than in the midwest, so proximity advantages will drive price fluctuations in sort of the same way that gravity turns those little CMBR bumps into galaxy clusters. At least until some other process (traffic?) limits....

I don't disagree with your basic point about the inevitability of a return to rationality in the housing market, but even at the national level the situation is much more complex than the back of the envelope can reveal, and I'm not sure how useful a story about national medians really is as an alternate narrative to the stories we all read about how insane things are in region X.

Steve

The way you save half the monthly mortgage payment is to rent a place that is much crappier than the place you want to buy, if you're in a market where housing price floor is set by rents as investment incomes (ie market rents are set by ability to cover mortgage and insurance costs plus small net return - this works if there is an interest rate spread between mortgages and investment loans).
So rent a minimal apartment, or get roomies, or something for a few years.

It is true that the median home buyer is above median household, but at the level of approximation I worked that is just a linear scaling.

A few percent of houses can be sustained at much higher prices, like Aspen.

I did mention intergenerational wealth transfer - if you bring more cash to the table you can get more house - either through lump sum down and same mortgage, or by showing unearned income.
Typically you're looking at grandparent inheritance, given timing with which people want to buy into markets. So there is some wealth dilution, both from splitting among multiple heirs, on average, and from draw down of accumulated assets during retirement.

The X and Y generations may start to see substantial leverage for housing from early boomer inheritance. Unless there is substantial wealth destruction.

You can have regional outliers, and I already noted that buying into bubbles is locally rational. But you can't avoid convergence to the mean in the long run.
You either have price convergence, or income inflation. Or both.

It looks like I should be able to afford a $45,000 home after maybe 6-10 years of saving. Assuming I never have an emergency which requires I use that savings before then. Oh, and I'm also supposed to be saving up 2-3 months-worth of income on the side, for said emergencies. Oh, and I'm supposed to be saving at least an additional $1000 a year for retirement. And let's not get into how I still don't have a car or private health insurance. And then there's my school, and the husband's school, and the child.

So... how exactly is the lower class supposed to achieve the "American Dream", again?

Unfortunately "just a linear scaling" can hide a lot, since a 50% adjustment on the median income and a 20% adjustment on the fraction of income that can go to housing, and suddenly you are talking of small houses that ought to go for $350k and rare expensive ones at $900k -- and that sounds a lot like California! I'm a great believer in convergence to the mean, I just wish I knew which mean we were destined to converge to!

The point about instabilities is a great one, though -- and there are also interesting ways that these instabilities get reinforced by outside actors (in Washington and on Wall St).

Yeah, going to 72,000 income you can buy more house.

I think the California markets made a mistake and overadjusted on the fraction of net income that could go to housing.
It is true that higher incomes may spend fractionally more of their income on housing, this is in part because some costs are independent of regional costs - eg car costs are roughly constant across geographic areas. But, ultimately you are cutting into discretionary spending, and then you have to ask what the point is in earning more but not having higher discretionary income to go with it....

I fear our solution has been chosen - asset deflation and then price inflation to cover nominal losses. Interesting question is if-and-when wage inflation catches up, or if there will be a permanent lowering of median standard of living.

Nerd: I am sorry - but you will not be able to afford a house in almost any are of the US on an income of $15,000 p.a. Even at 0% interest you still have to be able to pay back the principal!
You need higher income.
If you don't have inheritances, long term savings or serendipitous cash windfalls, you are very likely to need downpayments of about 20% for the next decade or more - there may be some programs to get people in with lower down, after the markets stabilize somewhat.
Once you have the higher income it then take of order 5 years to save enough for a downpayment, if you push hard at it.

"very likely to need downpayments of about 20% for the next decade or more"

Should but not true right now: FHA loans with 3.5 percent down still available at a mortgage dealer near you!

Why is "median income" tied to "median house price"? I'd assume that the lower income don't buy homes as much. Also the higher end probably doesn't pay in proportion to its income. My guess would be the former is more important than the latter due to the relative sizes of the populations in question. Probably a small correction though. It's not clear that the ratio scales well across income levels. I wonder what the historic ratio is? Especially for different income levels.

Well, as long as prices continue significant decline, any lender offering 3.5% down will face high probability of short term default, and will either require more down, or not be around to lend anymore. Even the Feds.

If I Recall Correctly, median housing prices have been around 3.5 times median income.
If income is approximately bounded below by zero, then the tail to very high income can't skew the offset too much.
Also, as noted, higher income tends to loan to higher proportion of income over a spread of incomes above median.
I'd say at very high income it is all cash purchase mostly, except a surprising fraction of very high income earners appear incapable of saving and have illiiquid investments.
Anecdotally...

A small linear scaling of, say, a factor of two on the size of US houses would bring US housing stock more into line with European housing stock. Small housing also acts as a brake on buying more and bigger stuff/junk. It would also significantly help energy consumption if people in the US lived in apartments instead of insisting on houses on two-acre lots (so that the nearest supermarket would be within walking distance instead of too far, as well as the direct heating and cooling savings). Since this kind of energy efficiency will be all but necessary in not many years time, there's an "I wouldn't start from here" feeling to the US housing stock.
On an individual basis, the total energy dollar cost of owning a home is spiking faster than other inflation, so heating/cooling, transport costs to work, to childcare, to food shopping, and to family and friends, should be very carefully factored into purchase decisions. The dollar price one should be willing to pay for a home that is energy inefficient in any of these areas should be heavily discounted. There is something of a bubble in good quality inner city housing as a result of people's perception of these pressures changing over the last year.

strangely enough I live in a smaller house within walking distance of work and shops
must be yoorpean roots
but, it came at a price premium, and I violated my own guideline on affordability, we'll soon find out if it was bought after bubbling started, or if equity buildup was adequate...
exciting times this side of the pond right now, 'course I hear there's some excitement both sides

Missing from the back of that envelope:

(1) Heterogeneity even within single Zip code. It is better to buy the worst house in a good neighborhood than a the best house in a bad neighborhood.

(2) Your distribution of estimated revenue and loss in extreme cases. If there is a chance of catastrophic failure of, say, your sole proprietorship, it may be good to homstead your property to cap what creditors can get.

(3) Whether you are single or married, and in a Community Property state or not.

(4) Many other considerations, but let's start with those, please.